Blues had trailed 1-0 with just seventeen minutes of the match at Pride Park remaining but an equaliser from Scott Dann and a stoppage time goal from Liam Ridgewell earned Blues a 2-1 win against Nigel Clough's side and a place in the sixth round for the first time in four years.
"We looked as if we were on our way out of the cup," McLeish said after the match.
"Derby troubled us before half-time and we didn't really get going until we made some changes.
"Once again the team demonstrated the fantastic determination they have produced time and time again this season.
"What we have to do now is maintain our form.
"If you get cocky and complacent the roof can cave in but we have got a lot of leaders in that dressing room."