Forest were unable to find a winner, however, meaning that the Rams claimed a valuable point from the East Midlands derby.
"It was totally absorbing," McClaren told Sky Sports News. "Not a classic in terms of football but for a local derby, that's never going to be with a lot at stake.
"Like I said at the beginning, you can't win unless you've got 11 players on the park. Once we equalised, I thought we'd go on to win it.
"Then we dropped to 10 men - the players were heroic at the end for a good 12-15 minutes. We had to adjust with 10 men and showed great character. It's a big point for us."
Next up for Derby is a home meeting with Blackburn Rovers in the Championship on Wednesday night.