Two first half goals by Cameron Jerome earned Blues a 2-1 win at Fratton Park - the league win coming just four days after they were beaten 2-0 by Pompey at the same venue in their FA Cup sixth round tie.
"We spoke before the game how Portsmouth might think our confidence had dropped and that maybe we don't have much to play for now this season in terms of our points tally already being at a good total," McLeish told Sky Sports News.
"But, the players were great and I thought they responded brilliantly.
"We kept the ball well and we had four or five chances in the first half when I thought we were fantastic."
The Blues boss also admitted to feeling a little apprehensive when Kanu scored what proved to be just a consolation goal in stoppage time for the hosts.
"I thought there was quite a few more minutes to go so it was a relief to hear the final whistle," he said.
"The defenders and goalkeeper were gutted in the dressing room because they are so proud of their shut-outs this season and they thought they were heading for another one."