diff --git a/python/ray/dag/compiled_dag_node.py b/python/ray/dag/compiled_dag_node.py
index 18a2e272b546..b1f3e51989a1 100644
--- a/python/ray/dag/compiled_dag_node.py
+++ b/python/ray/dag/compiled_dag_node.py
@@ -1431,7 +1431,9 @@ async def execute_async(
             fut = asyncio.Future()
             await self._fut_queue.put(fut)
 
-        return CompiledDAGFuture(self, self._execution_index, fut)
+        fut = CompiledDAGFuture(self, self._execution_index, fut)
+        self._execution_index += 1
+        return fut
 
     def teardown(self):
         """Teardown and cancel all actor tasks for this DAG. After this
diff --git a/python/ray/experimental/compiled_dag_ref.py b/python/ray/experimental/compiled_dag_ref.py
index 93f1397b60eb..e224250dfa77 100644
--- a/python/ray/experimental/compiled_dag_ref.py
+++ b/python/ray/experimental/compiled_dag_ref.py
@@ -92,7 +92,7 @@ def get(self, timeout: Optional[float] = None):
 
 
 @PublicAPI(stability="alpha")
-class CompiledDAGFuture(CompiledDAGRef):
+class CompiledDAGFuture:
     """
     A reference to a compiled DAG execution result, when executed with asyncio.
     This differs from CompiledDAGRef in that `await` must be called on the