United were favourites to leave Greece with a lead from the first leg of their Champions League game with Olympiacos, but nothing went to plan.
The Greeks ran out 2-0 winners, leaving United's hopes of qualifying for the quarter-finals hanging by a thread.
Moyes has had plenty to ponder during the week-and-a-half gap between that defeat and Saturday's Premier League game against West Brom.
He has addressed fans' concerns in a magazine column, and he has travelled across Europe to watch his players and some potential targets.
The Scot looked refreshed from the break when he addressed the media on Friday and he is convinced that the Olympiacos defeat will not have a lingering effect on his squad.
"It was a disappointing night in Olympiacos," the United manager said.
"None of us thought we would perform so poorly but since then we have picked ourselves up. We have had to recover and get ready for the next one."
In Moyes' letter, he thanked the fans for their support during a season which he admitted had gone far worse than he ever expected.
Moyes is happy that he has continued to receive the backing of the United support during his maiden season, but he acknowledges his team need to play better fast.
"The key is to improve all things," he said. "I want creativity and think the introduction of (Juan) Mata and his interplay with (Wayne) Rooney and Robin (van Persie) that I've seen recently has helped that creativity.
"I really believe the players are working hard for each other. They know they can play better and they will play better.
"Our play at times, I think, has been good but I don't think we've had the results and we need to get the results to improve, that's for sure."
Moyes will be in the rare position of playing a match where it is the opposition manager whose future is under the spotlight more than his own on Saturday.
Pepe Mel has failed to win during his six games in charge of the West Brom.
But United will not need to be reminded about the talented players Mel has at his disposal.
West Brom pulled off one of the shock results of the season in September when they beat United 2-1 at Old Trafford when Steve Clarke was in charge of the Baggies.
That defeat was an early sign that United were headed for stormy waters and Moyes does not want to lose to the Baggies again.
"Everyone keeps talking about the manager not winning for six games but West Brom won at Old Trafford this season and we need to try and avenge that and pick up the three points down there," the former Everton manager said.
One of the advantages of being out of the FA Cup is that Moyes knows victory for his team will put pressure on United's rivals.
A win would move United above Everton into sixth position, nine points off fourth place.
Although Moyes brushed off suggestions that Mel could be axed if the relegation-threatened Baggies lose.
"I'd be very surprised if Pepe Mel is under pressure at this moment," he said.
"I wouldn't think for one minute that after six games they were (thinking about) bringing in a new manager."
Clarke led West Brom to eighth in the league last season, but he was axed in December following a poor run of form.
Moyes admits he did not expect to see his compatriot sacked.
"I'm not privy to what goes on at West Brom but I thought he did a great job last year and had them in a lofty position in the Premier League," Moyes added.
"When I was at Everton last year, they were challenging us a lot of the time and he did really well so I'm surprised Steve left."