Blues had agreed a club-record fee to sign the France international, but they failed to reach agreement over his personal terms after a last-minute hitch.
McLeish told the club's official website: "We did everything that was asked of us and then the goalposts were moved at the last minute."
N'Zogbia has been linked with a move away from the DW Stadium all summer but Wigan manager Roberto Martinez criticised McLeish on Thursday for going public over his club's interest in the player - and claimed the Blues' offer at that point was less than one they rejected earlier in the summer.
But N'Zogbia was given permission to talk to the Midlands outfit after Wigan confirmed on Friday they had accepted a "much-improved" offer for the 24-year-old.
Those talks came to nothing, though, and McLeish added: "It was very important to us as a club to stick to our principals and look after the long-term interests of Birmingham City as we are custodians of the club.
"We remain ambitious and committed to adding extra quality to the playing squad but this deal became one that was not in the interests of the club.
"The Board worked with me extremely hard to try and get this one over the line and I thank them for their support."
N'Zogbia, who made his France debut earlier this month in Les Bleus' friendly defeat in Norway, started out in English football at Newcastle following his 2004 move from Le Havre.
He moved to Wigan in January 2009 after falling out of favour at St James' Park and was voted player of the season by players and fans at the DW Stadium last term.