News broke of Blackpool'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 his chairman Pete Winkelman to discuss the approach.
Following that meeting on Wednesday morning, the Milton Keynes club released the following statement: "It comes as no surprise that Karl's name is once again touted for one of the top managerial positions in the Championship as his bold and stylish brand of football has invited plenty of talk in the industry."
The statement continued: "Since being appointed at stadium:mk as the youngest manager in the Football League, Karl has guided our side to back-to-back play-off campaigns, broken a number of club records and only yesterday he created history by leading our club into the fourth round of the FA Cup for the first time.
"Karl is an ambitious, bright, young manager and he is firmly focused on realising MK Dons' dream of Championship football.
"Following discussions between Karl and the chairman, the club have turned down an approach from Blackpool to speak to Karl regarding the managerial vacancy at Bloomfield Road.
"Karl remains committed to the players, staff and, most importantly, the fans at Milton Keynes Dons, and will be looking to take the club from strength to strength by continuing to write new chapters in its history books.
"The club will not comment further on this matter."
Blackpool are looking for a new manager after Michael Appleton left to succeed Henning Berg at Blackburn.