A double from Kemar Roofe and goals from John Lundstram, Scott Wright and Ianis Hagi saw the Light Blues comfortably into the next round of the competition.
Speaking to RangersTV after the match, McAllister said: “All of the staff are very pleased, we asked for a response and a reaction prior to the game and I think we got that.
“We started the game ever so well and got ourselves in front nice and early and I think from there our attitude, level of play and some of the quality of our play was excellent.
“I thought we looked sharp in the first couple of minutes, we had the fans right behind us. They were excellent again so it just eased everybody down and we played with a lot of confidence after that.
“We played some really good attractive football but there was a nice snap and a nice bit of speed in our play especially going into the final third I thought some of our combination play was excellent.”
Rangers showed a relentless attitude this evening as they continued to push for more goals and McAllister was delighted to see goal threats throughout the squad.
He continued: “We totally respect our opponent, when we get in front we don't want to try and make the other team look foolish but we just stuck to what we do, we trust in what we do, we kept playing and I thought some of the play around the box was very good.
“I thought right throughout our team we had several goal threats, we were getting bodies in the box so it was a good night.
“It is so pleasing to see the fans back in and I think tonight they will go away and they've enjoyed the watch. I thought some of the play was excellent.”
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