Now City are nestling in a comfortable mid-table position and will be looking to extend their unbeaten league run to five games when they visit Wolves on Sunday.
McLeish said: "It has been some education over the last couple of years. We have had all the emotions from A to Z and I can't believe it has gone so quickly.
"We are at a decent level if you compare us to two years ago. I believe we have made substantial progress on and off the pitch and, with the support of the new board, believe we can continue to improve as a club.
"We are improving and have just that bit more quality than two years ago but it is a work in progress.
"I've managed to change things in central defence and the back four and I'm gradually beginning to change things in midfield and forward areas.
"There is a still a lot of team building to be done and we hope we can take a significant step to doing that in January.
"If we've got Premier League ambitions, we need to bring in the quality."
However, McLeish has cast doubts over whether he will be able to bring in Standard Liege striker Milan Jovanovic when the transfer window opens.
He said: "I've always admired Jovanovic but, whether he is a player that can come here or not, remains to be seen. I am sure he has got many admirers.
"From the fans' perspective it is brilliant to see us linked to players like that but I don't want to disappoint the fans.
"I can name another six big names that would really excite them but, if you don't get them, then you disappoint people.
"So I would rather keep my business private and move forward. We will see if something can be done there (with Jovanovic). I don't know. It is doubtful."
Blues have taken eight points from the last four games with Sunderland, Manchester City, Liverpool and Fulham.
But McLeish wants his players to maintain the performance level shown in those games when they tackle Wolves, Wigan, West Ham and Blackburn in the next month.
He said: "You've always got your apprehensions facing any opponent but I don't see why we can't go to Wolves with confidence.
"The players have been playing well but for the last few years we have yo-yoed between the divisions and I need the players not to have the mentality of playing well for two or three games and then taking a rest.
"We need to maintain the performance level at Wolves that we have shown in recent games.
"We are bullish about going to Wolves but we were bullish about going to Manchester United and Tottenham, but maybe there is less pressure in those games.
"This is a big pressure game and it will be interesting to see how the players handle that because Mick (McCarthy) will be smarting a little bit and he knows it is a big game for them.
"I am expecting them to come out of the blocks and we have to be ready for that challenge."
McLeish has no fresh injury worries and club captain Damien Johnson will be available after recovering from a hamstring injury.
Wolves 11/8, Birmingham 2/1, Draw 9/4