News broke of the Championship club's interest in Robinson on Tuesday night, shortly before both clubs were in action in FA Cup third-round replays.
After his side's 2-0 win over Sheffield Wednesday, Robinson revealed he planned to talk to Dons chairman Pete Winkelman to discuss the approach.
Following that meeting on Wednesday morning, the Milton Keynes club released a statement saying that they had turned down the Seasiders' request to speak to their manager.
Robinson felt it was important to reciprocate the loyalty that many of his players had shown him.
"The discussion was very, very short," the 32-year-old told the media ahead of his side's League One fixture at Crewe on Saturday.
"I think it's important nowadays that there is some loyalty. I think it's important that you do right by the people who pay your wages. Ultimately, my lifestyle is because of the chairman giving me an opportunity and the fans allowing that to come to fruition. I've got a debt of gratitude to pay to them.
"I asked for loyalty from these players - Darren Potter, Stephen Gleeson and Sam Baldock gave me tremendous loyalty. Izale McLeod showed me loyalty by coming back, Dean Lewington showed loyalty by constantly turning down things. Alan Smith showed loyalty by turning down millions of pounds to stay here. Shaun Williams could have gone but he showed his loyalty.
"It's important if the players are going to show it, that the manager and the staff are going to stand next to them and show it as well."
Blackpool are looking for a new manager after Michael Appleton left to succeed Henning Berg at Blackburn.