In what has been a testing debut campaign at the Old Trafford helm for Moyes, the Scot saw his troops suffer another crushing blow at Olympiakos on Tuesday.
A 2-0 defeat in the first leg of their UEFA Champions League last-16 encounter has left United with a mountain to climb if their continental quest is to continue.
And the latest setback in a miserable season has piled the pressure on Moyes, with the Scot now the favourite with Sky Bet to become the next Premier League manager to lose his job.
Moyes was 25/1 to be the next managerial casualty before United's latest loss, but his odds were repeatedly slashed on Wednesday morning, going from 11/1 to 5/6 in just over an hour.
Moyes concedes that the Red Devils failed to produce the required standard on Greek soil and paid the price, but he is refusing to throw in the towel and believes anything is still possible in the return date at Old Trafford.
He said: "It's the worst we've played in Europe, that's for sure. A really poor performance tonight. We never got going from the start and we didn't deserve anything because of the way we played tonight.
"We just never really got to grips with things. To a man, you could hardly pick anyone out, we just didn't perform. We came into the game in good form, a good mind set, but we didn't show that tonight.
"I still didn't think we were necessarily two goals worse off in the game. We had a shot that gets deflected, but we didn't offer enough on the night.
"I take responsibility, it's my team and I'll always front it up. We didn't play well tonight and we have to play better. We can do. The one good thing is that there is the second game to go.
"The players are hurting as well. They know how they performed. But there is a team here, that won't change, and we'll stick together.
"There is the second game to come and Old Trafford has seen some great nights in the past - I'm looking forward to hopefully seeing another one."
It was also a poor night for Robin van Persie who accused his Manchester United team-mates of getting in his way as he cut a frustrated figure in Greece.
Van Persie wasted a good chance to score a vital away goal at the end of the match and speaking to Dutch broadcaster NOS after the match, said that his cause was not helped by the positioning of some of his team-mates.
"It was quite difficult because my team-mates are often in the area where I want to play," the United striker said.
"That's why I have to change my tactics. Unfortunately, they are often in my area.
"It was much too slow today and we only had one shot on target in the whole match against Olympiakos, which is far too little. Everyone is very disappointed."
United have to win by three clear goals to be sure of their passage to the last eight of the competition but Van Persie is refusing to throw in the towel just yet.
"It is still possible, because with all due respect to Olympiacos, we should be able to win 3-0 at home," the striker added.
"It is not that they were fantastic (in the first leg), we just mostly failed."
Can United turn it around against Olympiakos? The second leg will be live on Sky Sports on March 19