Blues had to come from a goal behind to secure their place in the draw for the third round and when leading 3-1 the Blues boss expected the side to have won by a more comfortable margin.
However, Rochdale reduced the deficit to 3-2 with 15 minutes remaining and Blues had to dig in deep for their victory at St Andrews.
"We will try our best to go as far as we can," McLeish said after the match. It depends on the draw and you need a bit of luck but you never know.
"With the greatest respect to the Carling Cup, the Premier League is our greatest priority but we want to go far.
"We knew an upset could happen. You see teams stumble every year but at 3-1 I thought we would go on and score more.
"But credit to Rochdale as they fought back well."
McLeish was also pleased with the contribution made by recent signing Matt Derbyshire who marked his first start in a Blues shirt by scoring the third goal.
"Matt got brighter as the game went on," he said of the on loan from Olympiakos striker.
"You saw a glimpse of him when he got up the side from the first penetrating pass of the night and won the penalty.
"He started to look very dangerous in the second half in and around the box. He got his goal and linked up well."