He confirmed this week he is leaving the club after just one season, having failed to make his mark in Serie A.
On Totti, Enrique said: "It was a very special rapport right from the start. At the start of the training session after leaving him out, I'd assure him there was absolutely no problem. Quite the opposite.
"I made mistakes, of course. As a Coach I tried to make it easier for the players by preparing them for the game they had to face. There are many things that could be improved on and I am enormously disappointed when they didn't go well.
"I wish Roma a journey full of success. I have no complaints and if I made some mistakes, then I apologise. I'm convinced in Italy you can play beautiful football based on attack and I promise that I will improve in terms of defending. If I had stayed next season, I would've worked the same way. I continue to believe in this style of football."