The 32-year-old was a surprise appointment to the Milton Keynes helm in 2010 but his stock has risen considerably in that period. Robinson has been linked to a number of other clubs as a result and Blackpool made an approach for him earlier this month.
That move was blocked after talks with Winkelman, whose persuasive work paid dividends on Saturday as the League One promotion hopefuls secured the most famous victory in their short history - a 4-2 FA Cup fourth-round win at QPR to set up a fourth round clash with Barnsley.
"I am very pleased for Karl," the Dons chairman said. "You don't often get that much loyalty in football but he has shown the club a lot of loyalty in recent weeks and the players have just gone and thanked him on the pitch.
"If he had absolutely beaten me up to want to go and do something, of course I would have let him. But I discussed it with him and, in discussing with him, he wasn't going to jump on me to do something so I had the chance to talk him down.
"We talked about it and it was a no-brainer for me to reject the offer, the advance, at the end of the day.
"There will be offers because he is the best young manager in the Football League. We can see the way he gets his teams playing and we're proud of what we're achieving.
"I thought we had some fantastic performances from players as well, although my worry again is we're not at the end of January yet.
"I don't want to lose any of this team. I think this team has a chance to go up this year even though we didn't have a very good Christmas. This season is a long one and if you do have that quality you really do have a chance."