Sir Alex Ferguson's side started their new season with a 1-0 loss at Goodison Park on Monday but Pallister believes that Shinji Kagawa, Tom Cleverley and Robin van Persie will all begin to deliver soon.
The former Red Devils defender said: "That will be put to bed now. Let's look on the positives. Kagawa had a good debut and I think in Cleverley's appearance we saw the player we got last season before his injuries.
"I also fully believe that now Van Persie has got his debut out of the way and once the team gets to know him more we will have a better cutting edge.
"There is still plenty to be happy about."
United host Fulham at Old Trafford on Saturday afternoon.