Forrester made his debut for Rangers in the fourth round of the Scottish Cup at Ibrox in Glasgow, coming on as a substitute in the 62nd minute.
The 25-year-old attacking midfielder, who joined the Glasgow giants on a six-month loan deal from Doncaster Rovers earlier this month, helped his side win the tie 5-1.
Rangers boss Warburton has analysed the former Aston Villa prospect’s performance against the Scottish League One club, and has suggested that he was pleased.
“I think you saw there is a player who can play the way we want to play, he likes to get on the ball and his movement and technical ability is good,” the former Brentford manager told Rangers’ official website.
“He has an eye for goal and I like the fact he had a couple of shots, he had one miss but went again and I like that bravery. Harry made an impact but he has to fight for his place and he knows that.”
Over the course of the 90 minutes at Ibrox, hosts Rangers had as much as 69% of the possession, took 30 shots of which 14 were on target, and earned 12 corners.
Visitors Cowdenbeath had just 31% of the possession, took five shots of which one was on target, and earned two corners.
Rangers will return to action on Saturday afternoon when they take on Livingston at Ibrox in the Scottish Championship.