diff --git a/sphinx/domains/__init__.py b/sphinx/domains/__init__.py
index 4064b7eaf75..f564367d867 100644
--- a/sphinx/domains/__init__.py
+++ b/sphinx/domains/__init__.py
@@ -13,7 +13,7 @@
 from sphinx.locale import _
 
 if TYPE_CHECKING:
-    from collections.abc import Callable, Iterable, Sequence, Set
+    from collections.abc import Iterable, Sequence, Set
     from typing import Any
 
     from docutils import nodes
@@ -108,8 +108,8 @@ class Domain:
 
     def __init__(self, env: BuildEnvironment) -> None:
         self.env: BuildEnvironment = env
-        self._role_cache: dict[str, Callable] = {}
-        self._directive_cache: dict[str, Callable] = {}
+        self._role_cache: dict[str, RoleFunction] = {}
+        self._directive_cache: dict[str, type[Directive]] = {}
         self._role2type: dict[str, list[str]] = {}
         self._type2role: dict[str, str] = {}
 
@@ -181,7 +181,7 @@ def role_adapter(
         self._role_cache[name] = role_adapter
         return role_adapter
 
-    def directive(self, name: str) -> Callable | None:
+    def directive(self, name: str) -> type[Directive] | None:
         """Return a directive adapter class that always gives the registered
         directive its full name ('domain:name') as ``self.name``.
         """
diff --git a/sphinx/util/docutils.py b/sphinx/util/docutils.py
index faa0695c9fe..5a26bc88e10 100644
--- a/sphinx/util/docutils.py
+++ b/sphinx/util/docutils.py
@@ -19,7 +19,7 @@
 from docutils.utils import Reporter, unescape
 
 from sphinx.errors import SphinxError
-from sphinx.locale import _, __
+from sphinx.locale import __
 from sphinx.util import logging
 from sphinx.util.parsing import nested_parse_to_nodes
 
@@ -263,51 +263,44 @@ class sphinx_domains(CustomReSTDispatcher):
     """
 
     def __init__(self, env: BuildEnvironment) -> None:
-        self.env = env
+        self.domains = env.domains
+        self.current_document = env.current_document
         super().__init__()
 
-    def lookup_domain_element(self, type: str, name: str) -> Any:
-        """Lookup a markup element (directive or role), given its name which can
-        be a full name (with domain).
-        """
-        name = name.lower()
+    def directive(
+        self,
+        directive_name: str,
+        language_module: ModuleType,
+        document: nodes.document,
+    ) -> tuple[type[Directive] | None, list[system_message]]:
+        """Lookup a directive, given its name which can include a domain."""
+        directive_name = directive_name.lower()
         # explicit domain given?
-        if ':' in name:
-            domain_name, name = name.split(':', 1)
-            if domain_name in self.env.domains:
-                domain = self.env.get_domain(domain_name)
-                element = getattr(domain, type)(name)
+        if ':' in directive_name:
+            domain_name, _, name = directive_name.partition(':')
+            try:
+                domain = self.domains[domain_name]
+            except KeyError:
+                logger.warning(__('unknown directive name: %s'), directive_name)
+            else:
+                element = domain.directive(name)
                 if element is not None:
                     return element, []
-            else:
-                logger.warning(
-                    _('unknown directive or role name: %s:%s'), domain_name, name
-                )
         # else look in the default domain
         else:
-            def_domain = self.env.current_document.default_domain
-            if def_domain is not None:
-                element = getattr(def_domain, type)(name)
+            name = directive_name
+            default_domain = self.current_document.default_domain
+            if default_domain is not None:
+                element = default_domain.directive(name)
                 if element is not None:
                     return element, []
 
         # always look in the std domain
-        element = getattr(self.env.domains.standard_domain, type)(name)
+        element = self.domains.standard_domain.directive(name)
         if element is not None:
             return element, []
 
-        raise ElementLookupError
-
-    def directive(
-        self,
-        directive_name: str,
-        language_module: ModuleType,
-        document: nodes.document,
-    ) -> tuple[type[Directive] | None, list[system_message]]:
-        try:
-            return self.lookup_domain_element('directive', directive_name)
-        except ElementLookupError:
-            return super().directive(directive_name, language_module, document)
+        return super().directive(directive_name, language_module, document)
 
     def role(
         self,
@@ -316,10 +309,34 @@ def role(
         lineno: int,
         reporter: Reporter,
     ) -> tuple[RoleFunction, list[system_message]]:
-        try:
-            return self.lookup_domain_element('role', role_name)
-        except ElementLookupError:
-            return super().role(role_name, language_module, lineno, reporter)
+        """Lookup a role, given its name which can include a domain."""
+        role_name = role_name.lower()
+        # explicit domain given?
+        if ':' in role_name:
+            domain_name, _, name = role_name.partition(':')
+            try:
+                domain = self.domains[domain_name]
+            except KeyError:
+                logger.warning(__('unknown role name: %s'), role_name)
+            else:
+                element = domain.role(name)
+                if element is not None:
+                    return element, []
+        # else look in the default domain
+        else:
+            name = role_name
+            default_domain = self.current_document.default_domain
+            if default_domain is not None:
+                element = default_domain.role(name)
+                if element is not None:
+                    return element, []
+
+        # always look in the std domain
+        element = self.domains.standard_domain.role(name)
+        if element is not None:
+            return element, []
+
+        return super().role(role_name, language_module, lineno, reporter)
 
 
 class WarningStream: