But he felt the move was mutually beneficial for both the 22-year-old defender and The U's, who he represented 35 times having joined from St Patrick’s Athletic in January 2021.
"Luke's an interesting one because you can imagine everyone getting a little bit frustrated with us selling a player," said Robinson. "This is right for the football club at the end of the day. This is something that the shareholders asked me as well and I thought it was the right decision.
"When a player comes to you and he wants to leave, to a team that has just been relegated from the Premier League, and wants to get back there within 12 months, there aren't many teams at that level that you'd jump at that quickly, it was right for him."
The 41-year-old also commended the conduct of the Irish centre back after his switch to Turf Moor, on a four-year deal, was confirmed. The youngster, who scored four times in League One last season, became Vincent Kompany's second signing as Clarets boss.
Robinson said: "The price was very good and very aggressive in respect of what we felt was right for him. We wish him all the luck in the world. The way he said 'goodbye' was sensational.
"He looked you in the eye and he meant it, so it was nice in the way he conducted himself with that. Some players have left and not said a word to anybody. He got it back on and we wish him all the luck in the world.
“Luke had been a credit to himself and his family. It’s not always easy to make the adjustment from part time football to playing and training every day but he made that step up very quickly and I think the fans could all see the potential he has. Burnley are a terrific club and we wish him well.”