The Light Blues manager watched on as his men worked the visiting rearguard hard in the Scottish Premiership fixture before Alfredo Morelos netted a deserved opener two minutes before the break before Ryan Kent made it 2-0 not too long after the interval.
Speaking afterwards to RangersTV, van Bronckhorst said: "Defending like St Johnstone did, it will cost a lot of energy and eventually, their energy levels will go down and then we can attack the spaces more and spaces they ultimately will leave us, and I think we did that really well in the second half.
"It was the game we expected - a tough game with a good, well-organised St Johnstone who are bottom of the league, but today, I think they had a really good performance.
"I think we started really well and created some good chance to go one-up, but we didn't make the chances into goals and after that, we didn't create as much and it was difficult to find the spaces, and scoring to make it 1-0 just before half time was very important.
"Then in the second half, we were able to play a little bit more the way we want - finding three players between the lines and getting the passing game we want to stretch the opponent.
"We created some good chances and also scored a good goal from one move."
Van Bronckhorst also took time to look ahead to Saturday’s visit of Dundee United to Ibrox, adding: "We will have another two days of rest which we had before and now it is time to prepare well for Dundee United on Saturday.
"We have to be there at three o'clock so we will prepare the team well and from the whistle, we go all in."
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