The Dons crashed out of the William Hill Scottish Cup with a 1-0 defeat at Hibernian which, following a Scottish Communities League Cup exit to St Mirren last October, leaves them without the prospect of a Hampden final this season.
Craig Brown's side, sitting in sixth place in the SPL, are without a win in five games but former Fulham midfielder Milsom, 26, is looking for a return to form against the Buddies at Pittodrie on Saturday.
"I thought we were the better team last week and were the better team the week before but didn't get the win, but that's football," Milsom said.
"We are out of the cup competitions, it is massively disappointing and hard to take but there is still a lot to play for.
"We have to get last week out of our head, put it behind us, move on in a positive frame of mind and try to finish as high as we can in the league.
"We need to finish in those places where we qualify for Europe, so pushing up to second and third is a must for us.
"St Mirren will come here full of confidence but it is important that we get at them and get the three points."
Four out of Aberdeen's next five SPL games are at home and Milsom is hoping that Pittodrie will be the place to repay the club's travelling support for their backing this season.
"It is a big opportunity and it is important that the fans come to see us," he said.
"You can understand their frustration, coming down in the numbers they did to Hibs, and not just to that game, but throughout the season.
"I just hope they stick by us and hopefully we can repay their faith."