diff --git a/airflow/providers/cncf/kubernetes/operators/pod.py b/airflow/providers/cncf/kubernetes/operators/pod.py
index d530f86bcc3ae..ef5366d6c4030 100644
--- a/airflow/providers/cncf/kubernetes/operators/pod.py
+++ b/airflow/providers/cncf/kubernetes/operators/pod.py
@@ -36,6 +36,7 @@
 import tenacity
 from deprecated import deprecated
 from kubernetes.client import CoreV1Api, V1Pod, models as k8s
+from kubernetes.client.exceptions import ApiException
 from kubernetes.stream import stream
 from urllib3.exceptions import HTTPError
 
@@ -788,9 +789,18 @@ def _clean(self, event: dict[str, Any]) -> None:
         # Skip await_pod_completion when the event is 'timeout' due to the pod can hang
         # on the ErrImagePull or ContainerCreating step and it will never complete
         if event["status"] != "timeout":
-            self.pod = self.pod_manager.await_pod_completion(
-                self.pod, istio_enabled, self.base_container_name
-            )
+            try:
+                self.pod = self.pod_manager.await_pod_completion(
+                    self.pod, istio_enabled, self.base_container_name
+                )
+            except ApiException as e:
+                if e.status == 404:
+                    self.pod = None
+                    self.log.warning(
+                        "Pod not found while waiting for completion. The last status was %r", event["status"]
+                    )
+                else:
+                    raise e
         if self.pod is not None:
             self.post_complete_action(
                 pod=self.pod,
@@ -817,11 +827,11 @@ def _write_logs(self, pod: k8s.V1Pod, follow: bool = False, since_time: DateTime
                 line = raw_line.decode("utf-8", errors="backslashreplace").rstrip("\n")
                 if line:
                     self.log.info("[%s] logs: %s", self.base_container_name, line)
-        except HTTPError as e:
+        except (HTTPError, ApiException) as e:
             self.log.warning(
                 "Reading of logs interrupted with error %r; will retry. "
                 "Set log level to DEBUG for traceback.",
-                e,
+                e if not isinstance(e, ApiException) else e.reason,
             )
 
     def post_complete_action(self, *, pod, remote_pod, **kwargs) -> None:
diff --git a/tests/integration/executors/test_celery_executor.py b/tests/integration/executors/test_celery_executor.py
index 72e9ca9e10b1f..2b72d2e91d1a2 100644
--- a/tests/integration/executors/test_celery_executor.py
+++ b/tests/integration/executors/test_celery_executor.py
@@ -23,6 +23,7 @@
 import os
 import sys
 from datetime import datetime
+from time import sleep
 from unittest import mock
 
 # leave this it is used by the test worker
@@ -42,6 +43,8 @@
 from airflow.utils.state import State
 from tests.test_utils import db
 
+logger = logging.getLogger(__name__)
+
 
 def _prepare_test_bodies():
     if "CELERY_BROKER_URLS" in os.environ:
@@ -145,7 +148,15 @@ def fake_execute_command(command):
                     executor.task_publish_retries[key] = 1
 
                 executor._process_tasks(task_tuples_to_send)
-
+                for _ in range(20):
+                    num_tasks = len(executor.tasks.keys())
+                    if num_tasks == 2:
+                        break
+                    logger.info(
+                        "Waiting 0.1 s for tasks to be processed asynchronously. Processed so far %d",
+                        num_tasks,
+                    )
+                    sleep(0.4)
                 assert list(executor.tasks.keys()) == [
                     ("success", "fake_simple_ti", execute_date, 0),
                     ("fail", "fake_simple_ti", execute_date, 0),
diff --git a/tests/providers/cncf/kubernetes/operators/test_pod.py b/tests/providers/cncf/kubernetes/operators/test_pod.py
index 8b7c238e9c143..f7a8e24d6973d 100644
--- a/tests/providers/cncf/kubernetes/operators/test_pod.py
+++ b/tests/providers/cncf/kubernetes/operators/test_pod.py
@@ -25,7 +25,7 @@
 import pendulum
 import pytest
 from kubernetes.client import ApiClient, V1Pod, V1PodSecurityContext, V1PodStatus, models as k8s
-from kubernetes.client.rest import ApiException
+from kubernetes.client.exceptions import ApiException
 from urllib3 import HTTPResponse
 
 from airflow.exceptions import (
@@ -2062,6 +2062,28 @@ def test_async_write_logs_should_execute_successfully(
         else:
             mock_manager.return_value.read_pod_logs.assert_not_called()
 
+    @patch(KUB_OP_PATH.format("post_complete_action"))
+    @patch(KUB_OP_PATH.format("client"))
+    @patch(KUB_OP_PATH.format("extract_xcom"))
+    @patch(HOOK_CLASS)
+    @patch(KUB_OP_PATH.format("pod_manager"))
+    def test_async_write_logs_handler_api_exception(
+        self, mock_manager, mocked_hook, mock_extract_xcom, post_complete_action, mocked_client
+    ):
+        mocked_client.read_namespaced_pod_log.side_effect = ApiException(status=404)
+        mock_manager.await_pod_completion.side_effect = ApiException(status=404)
+        mocked_hook.return_value.get_pod.return_value = k8s.V1Pod(
+            metadata=k8s.V1ObjectMeta(name=TEST_NAME, namespace=TEST_NAMESPACE)
+        )
+        mock_extract_xcom.return_value = "{}"
+        k = KubernetesPodOperator(
+            task_id="task",
+            get_logs=True,
+            deferrable=True,
+        )
+        self.run_pod_async(k)
+        post_complete_action.assert_not_called()
+
     @pytest.mark.parametrize(
         "log_pod_spec_on_failure,expect_match",
         [