The presence of Sir Alex Ferguson in the visitors' dressing room after Wednesday's five-goal Champions League hammering of Bayer Leverkusen was a further reminder of the standards Moyes is being asked to live up to at Old Trafford.
It has not been an easy ride so far, with an awful transfer window and poor early results at Liverpool and Manchester City, which were followed by a home loss to West Brom.
Slowly though, Moyes is getting to grips with the task.
United are now 11 games unbeaten and though the loss of two points at Cardiff last Sunday kept them out of the Champions League spots for another week, the size of the win in Germany has put a smile back on the Red Devils faces.
And Evans believes Moyes has had a positive impact.
"The new manager is very tactically aware," said the Northern Ireland international.
"He is definitely improving the team in the sense of how he wants to play and the tactics he wants.
"The things he is teaching us can only benefit the players.
"It is maybe taking us a bit more time than we would have liked but performances like that beating Leverkusen show things are knitting together a bit more."
Evans does accept one good result means nothing and knows that only when United have been on one of the sustained surges they are so famous for will doubts about them start to disappear.
However, at the launch of his autobiography, Ferguson said United were the only club capable of winning the championship from a position that, at the time, was worse than the one they are in now.
And, as neither Manchester City nor Chelsea have been significantly better, Arsenal are the ones who are now having the questions asked of them.
"We haven't always led the league from the front but Arsenal are now in a position they haven't been in for a number of years," said Evans.
"It is quite a strange league because everyone is taking points off each other.
"Obviously there are a lot of new managers and of the top teams Arsene Wenger is the only one who has been there for a long time.
"Maybe that shows."
United have the chance to bounce back from the loss of those points at Cardiff last weekend by beating Tottenham on Sunday.
White Hart Lane has been a productive ground for United in the past.
However, they have never had to go there when the hosts are trying to recover from a 6-0 pasting such as the one they suffered at Manchester City.
And Evans is more than a little wary.
"They will be pretty motivated," said Evans.
"Leverkusen have lost by a big score against us but they won't lose their next game by a big score.
"Watching the Spurs-City game at the weekend, Spurs' heads went down after a couple of goals.
"They will be looking for a fresh start on Sunday, especially at White Hart Lane which is always a tough place to go."