Dons chairman Pete Winkelman has dismissed an approach from the Blues for the 34-year-old.
"I'm flattered - but just as flattered by the chairman's response. It shows he wants me at this football club," Robinson told BBC Three Counties Radio.
"That gives me the satisfaction of knowing you're wanted somewhere."
Robinson has been in charge at Stadium MK since May 2010 and is the fourth longest-serving manager across the Premier League and Football League.
He has finished in the play-offs in two of his four full seasons in charge, but has yet to win promotion from League One.
Championship side Birmingham sacked manager Lee Clark on Monday and are 21st in the table.
"[The approach] has come as a shock and I think everyone has conducted themselves wonderfully well," said Robinson after his side's 2-1 win over Fleetwood on Tuesday, which moved them up to fourth.
"It's something I didn't want to get out there. It's happened and the chairman said 'no' and we move on.
"To be linked to a club like Birmingham City - it's a massive football club in one of the biggest cities in the UK.
"People talk about my name being in for this or that - it's nothing to do with me. The fact that people go to the chairman means I have to answer these questions.
"My wife and daughter are extremely happy here and we stroll on at MK Dons."
MK Dons boss Karl Robinson has said he is "flattered" by Birmingham City's interest in his services and his own club's desire to keep him.