The Cup exit followed Saturday's home defeat to Newcastle United.
"I have got a real job on and I need to get down to work and really start to manage," Moyes confessed after this latest demoralising defeat.
"But I'll take the responsibility, I'll pick the team and I'll be in the same place next week on the side of the pitch. So people will still be able to see me.
"Of course I am concerned. Any manager would be in this position.
"We want to get points on the board and we don't want to be getting knocked out of cup competitions like this."