Moyes is still clinging to his job and Rooney admits United have struggled to overcome the loss of Sir Alex Ferguson following his decision to retire as boss last summer.
He said: "I think it was always going to be tough when Sir Alex left. It was obviously a massive change so we knew it was going to be tough, but we didn't expect it to be as tough as it has been.
"But we have to put that right. We have to keep working, keep believing in ourselves and hopefully it'll get better.
"The players talk after every game, whether we win, lose or draw, but we knew as a team what went wrong on Sunday - we didn't need anyone to tell us, and we came out and delivered a big performance.
"If it's not going right, some games you can have bad games, but you still need to put that effort in. It's massively important to me, to the team and the manager.
"Sometimes it may not look like that, but we are giving everything. We are trying. Sometimes it doesn't happen but we are working hard to get better and to try to climb the table."
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