diff --git a/changelogs/fragments/40424_postgresql_db_not_failed_when_dump_err.yml b/changelogs/fragments/40424_postgresql_db_not_failed_when_dump_err.yml
new file mode 100644
index 00000000000..9be407bf4ea
--- /dev/null
+++ b/changelogs/fragments/40424_postgresql_db_not_failed_when_dump_err.yml
@@ -0,0 +1,2 @@
+bugfixes:
+  - postgresql_db - the module fails not always when pg_dump errors occured (https://github.com/ansible/ansible/issues/40424).
diff --git a/lib/ansible/modules/database/postgresql/postgresql_db.py b/lib/ansible/modules/database/postgresql/postgresql_db.py
index 89cd7c4ea18..db4fbd3ba54 100644
--- a/lib/ansible/modules/database/postgresql/postgresql_db.py
+++ b/lib/ansible/modules/database/postgresql/postgresql_db.py
@@ -501,9 +501,16 @@ def main():
             try:
                 rc, stdout, stderr, cmd = method(module, target, target_opts, db, **kw)
                 if rc != 0:
-                    module.fail_json(msg=stderr, stdout=stdout, rc=rc, cmd=cmd)
+                    module.fail_json(msg='Dump of database %s failed' % db,
+                                     stdout=stdout, stderr=stderr, rc=rc, cmd=cmd)
+
+                elif stderr and 'warning' not in str(stderr):
+                    module.fail_json(msg='Dump of database %s failed' % db,
+                                     stdout=stdout, stderr=stderr, rc=1, cmd=cmd)
+
                 else:
-                    module.exit_json(changed=True, msg=stdout, stderr=stderr, rc=rc, cmd=cmd)
+                    module.exit_json(changed=True, msg='Dump of database %s has been done' % db,
+                                     stdout=stdout, stderr=stderr, rc=rc, cmd=cmd)
             except SQLParseError as e:
                 module.fail_json(msg=to_native(e), exception=traceback.format_exc())