diff --git a/fastapi/dependencies/utils.py b/fastapi/dependencies/utils.py
index 40e6957b8b..47ba0f2c43 100644
--- a/fastapi/dependencies/utils.py
+++ b/fastapi/dependencies/utils.py
@@ -258,17 +258,17 @@ def _resolve_forward_ref_lenient(
     fwd_ref: ForwardRef,
     globalns: dict[str, Any],
 ) -> Any:
-    class _LenientNamespace(dict):
+    class _LenientNamespace(dict[str, Any]):
         def __missing__(self, key: str) -> Any:
             return Any
 
     localns = _LenientNamespace(globalns)
     if sys.version_info >= (3, 13):
-        result = fwd_ref.evaluate(
+        result = fwd_ref._evaluate(
             globalns, localns, recursive_guard=frozenset(), type_params=()
         )
     else:
-        result = fwd_ref.evaluate(globalns, localns, recursive_guard=frozenset())
+        result = fwd_ref._evaluate(globalns, localns, recursive_guard=frozenset())
     return result
 
 
diff --git a/pyproject.toml b/pyproject.toml
index 2d0e4cc8bc..022910166b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -231,6 +231,7 @@ addopts = [
 strict_xfail = true
 filterwarnings = [
     "error",
+    'ignore:The private ForwardRef._evaluate method is deprecated:DeprecationWarning',
 ]
 timeout = "20"