Forrester, who joined Rangers from Doncaster Rovers in December, started the Scottish Cup quarter-final tie at Ibrox and played for 73 minutes.
The 25-year-old attacking midfielder scored as early as the first minute, as the Gers won the encounter 4-0 to book their place in the semi-finals of the prestigious cup competition.
Warburton was impressed with Forrester’s display and with the overall performance of his team.
“We wanted to make sure that we maintained our own tempo during the match and worked at our intensity,” the Englishman told Rangers’ official website.
“From the first whistle we worked hard and got the ball and it was tremendous work from Forrester, but all round today and over there were great performances.”
Over the course of the 90 minutes at Ibrox on Saturday afternoon, hosts Rangers had 56% of the possession, took 12 shots of which eight were on target, and earned 13 corners.
Visitors Dundee had 44% of the possession, took 15 shots of which only four were on target, and earned six corners.
Rangers will return to action on Friday evening when they take on Greenock Morton at Ibrox in Glasgow in the Scottish Championship.