Barry Ferguson's 62nd minute goal, his first since joining the club last summer, helped Blues to a 1-0 victory against Billy Davies' Championship outfit and set up a fourth round away tie against Everton.
"I'm happy to get the victory from a tough game when we weren't at our best," McLeish said after the game at St Andrews on Tuesday night.
"Once again it tells you a lot about the resilience of the players that we can come out on top when not firing on all cylinders - and it was a terrific goal. That was vintage Barry, with the run and finish.
"But I have to say that Forest played well and they can count themselves unlucky to be out of the Cup.
"I wanted to keep the momentum going that we have at present so I kept the same team (that played against Manchester United at the weekend).
"The players have not been training recently because of the weather so it is better that they play rather than have two or three days off and lose their sharpness.
"It was important they played tonight with a view to Saturday's game against Portsmouth."