A ‘bit of magic’ from Ianis Hagi gave Gers the breakthrough and proved to be the difference in the 1-0 victory at Ibrox.
Speaking to RangersTV at full-time, McAllister said: “I thought in the second half we hit a wee bit more rhythm, I thought St Johnstone made it difficult. They are very well organised and very well drilled.
“They set-up how we thought they would but we still found it difficult to play through them.
“There were good parts of the game where I thought we showed control, I thought at times Joe Aribo was excellent but I thought it took a bit of magic from Ianis Hagi to make the difference but it was a big three points again."
With 21 clean sheets this season, McAllister praised the organisation shown by the team out of possession.
He continued: “Flair, technique, playing on the front foot and actually trying to make things look that pretty is all well and good but there are two sides to the game.
“You look at all top-level football nobody gets a free ride so out of possession you have got 10 outfield players who have got to do their duty.
“They have got a specific job in the team to try and keep the ball out of our goal and I think that is what we have shown throughout this season. Our organisation when we are out of possession has been pretty good.”
There were two changes to the starting line-up this evening with Kemar Roofe and Ianis Hagi coming in for Glen Kamara and Alfredo Morelos.
With changes seamlessly slotting into the squad this season, McAllister said it shows the team spirit in the group.
He explained: “I thought the most wonderful example of that being shown was last week at Easter Road. Ryan Kent went and pressed three or four guys in the 93rd minute and all of our bench who were sitting behind us in the in the stand stood up and clapped Ryan Kent.
“That just shows that there are 18 or 19 guys all pulling together which is massive.
“We miss our fans dearly and the run we are on I'm sure if the Rangers fans were in Ibrox tonight they would be loving it but there are advantages.
“In key moments of the game crucial information does get on and I think just watching us in the last five or six games we have finished the game very strong.
“I think that comes from the energy from the side from subs, coaches, manager just trying to push the guys through to keep the three points.”
Scottish