The Spain international completed a £37.1m move to Manchester United on Saturday after failing to secure a regular place in the Chelsea side under Mourinho, despite being named the club's player of the season for the last two years.
Mourinho has preferred Oscar to Mata and he admitted he had no choice but to sell Mata after forcing him to play out of position.
"I am sorry that I didn't make him a stronger player. Maybe it was something new for him, not to be a first choice (player) in a difficult moment," said Mourinho.
"Maybe that made him, as a man, as a player, stronger but I gave him nothing to be honest and I feel sorry with that.
"I tried to make him play in a position where he was not comfortable. He gave everything and played some good matches in that position.
"We are speaking about a world champion, a European champion. It is difficult for him.
"I feel sorry for that and because of that I feel we couldn't stop him going to Manchester United, despite being Manchester United's direct rival."
United boss David Moyes expects the Spanish playmaker to give his side a huge lift in their bid to finish in the top four.
"This is the first, and there will be many more to come in time. I want the quality of Juan to be the start of it," Moyes told MUTV.
"I don't think we will have any more (new signings) in January - I'm still working on it and looking to do so. But hopefully it will be the first of some new signings, some new players who will arrive, more likely in the summertime.
"Undoubtedly we could all do with a bit of a lift. We have not done as well as we would have liked to do. We see this as the start, we have to look to improve and I'm going to try to bring in some new players to make that happen.
"I want to build an exciting team, I want to win and I want to give the supporters something to shout about - I've not done that often enough."
Moyes, who is likely to give Mata his debut at home to Cardiff on Tuesday, admitted he was surprised to be able to get the player in mid-season.
"I never felt that we would get that opportunity," added the Scot. "I wasn't sure that Chelsea would ever sell him to us. Thankfully we got there and I am delighted he is here.
"I'm a bit surprised because it's not something that tends to happen especially between Premier League teams. I was surprised when it happened but we have got a really exciting player, a player I'm looking forward to working with, a player I think everybody in football looked at and says he did a great job for Chelsea.
"I'm looking forward to seeing him in a red jersey and doing it for us."
Juan Mata will be presented as Manchester United's record signing in a news conference on Sky Sports News from 1:30pm. You can also follow coverage in our Sky Sports Today live blog