Six Airdrie players received cautions from referee Greg Aitken at Excelsior Stadium as they were narrowly beaten 1-0 by the Ibrox club.
Their Gers counterparts were deeply unhappy with the treatment they were subjected throughout the match despite the victory.
But Bollan, who was involved in a bust-up with Rangers centre-half Bilel Mohsni at the end of the game, was delighted with the attitude of his charges during the game. He said: "We had to let Rangers know they were in a game with the quality they have got and my players did that.
"We told them they would have to be in the Rangers players' faces and they were. They battled away great and I am proud of them."
Bollan refused to confirm what Mohsni had said to him in heated exchanges on the pitch after the final whistle. He said: "I was dragging my players off the pitch when he gave me an earful."
Bollan added: "The performance was positive. We are now two points behind the team in front and our aim at the minute is to catch them."