Mackay-Steven feels Celtic will be raring to bounce back after some missed chances and defensive errors undermined an impressive overall display in their 3-0 home loss on Tuesday night.
Celtic have faltered after a number of Champions League games this season but Mackay-Steven, whose team lost 4-0 at Celtic Park last month, said: "I think it will be as difficult as it always is. Going to Parkhead is never easy and they will be looking to get a positive result after what happened on Tuesday."
He continued: "They will be at the races so we need to make sure we are. They will be right up for the game. I felt they played well on Tuesday night and were unlucky to lose 3-0.
"They will definitely be looking to bounce back so we will need to perform as well as we can to get anything from the game."
United go into the game on a high after recording two victories and six goals, against Rangers and Hearts, in their opening two matches under Jackie McNamara. Mackay-Steven said: "We will be confident, we have done well in the last few games.
"Hopefully we can start off well and keep that going. Not too much has changed. The manager has come in with a few different ideas in training. He is great to work with and speaks well to the boys.
"Everyone is flying in training and enjoying it again. Peter Houston did a great job as well but the new manager has his own ideas and it has been a fresh start for everyone, even the boys that have not been playing.
"It's a fresh chance for everyone to prove themselves and it has kept everyone on their toes."
The former Liverpool and Airdrie player has made five successive starts after coming back from a broken hand, his second injury lay-off this season. The 23-year-old said: "I'm pretty much there or thereabouts. I have had quite a lot of games under my belt now and been training well, so I feel nearly 100% now."