The Light Blues were fantastic in defeating Willem II 4-0 to reach the Europa League play-off round, where they will face Turkish giants Galatasaray.
McAllister told this afternoon’s press conference: "When you go into a game, you're always looking to get the right result and if you can manage to get that right result and play pretty well, then that is a good double-whammy.
"So we are pleased on both points. I thought we managed the game pretty well - we had identified they had some threat in the attacking areas and the first 10 or 15 minutes, they started the game pretty well but when we bedded in and stated to get control of the ball, I thought we played pretty well.
"It was nice to see the goals go in close together and then we managed the game pretty well after that."
The clean sheet part of last night’s win was down, in no small part, to the performance of Allan McGregor in goal for Rangers.
He made a string of top-class saves, and McAllister continued: "I thought in the early stages of the game, Allan made a wonderful save, and then in the second half, a couple of great saves.
"Coming back in, I thought he showed a real, strong mentality as well with his focus - he is a guy who plays with pure emotion and passion - passion for this club - but I thought his mentality and his ability to make a crucial save, it served us really, really well in these European campaigns.
"He seems to have done it at quite a few away grounds and in-terms of moving forward, we have two very good goalkeepers."
Rangers will have to refocus on Motherwell at Fir Park on Sunday, but McAllister took a moment to look ahead to the visit of Galatasaray to Ibrox on Thursday.
He said: "It is a great shame the world is in the situation it's in as a two-legged affair, going to that stadium and Galatasaray coming here, it would have been two great games for both sets of fans.
"But, we have managed to get past Willem and we have been fortunate to get a home draw against Galatasaray.
"Looking at the profile of some of the players, you would maybe just have them ahead, but they are traveling to us and it is one game and we are really looking forward to it.
"We are on a nice run of form, we have defended our goal well and we look a threat going forward.
"So we welcome Galatasaray when they come here on Thursday - it is going to be a tough game and we will have to be at our very, very best to get the right result."