Chelsea were regarded as favourites to sign Shaw as a replacement for Ashley Cole throughout the summer with the England international a boyhood Blues fan.
However, Chelsea shelved their interest in Shaw to leave the path clear for United to sign the left-back from Southampton for a fee in the region of £27million.
Chelsea opted to sign Atletico Madrid full-back Filipe Luis instead of Shaw and Mourinho claims a deal for the 19-year-old would have "killed" the club due to UEFA's Financial Fair Play rules and possibly caused unrest in the Stamford Bridge dressing room.
"If we pay to a 19-year-old boy what we were being asked for, for Luke Shaw, we are dead," said Mourinho.
"We kill our stability with financial fair play. We kill the stability in our dressing room.
"Because when you pay that much to a 19-year-old kid — a good player, a fantastic player — but when you pay that amount of money, the next day the players knock on the club's door.
"They would have been saying 'How is it possible I play for this club 200 games and won this and that; how come a 19-year-old comes here and gets more money than I get?' It would kill immediately our balance and we don't allow that.
"Filipe's much less expensive. And a guy like Filipe Luis played for Brazil, won titles in Spain, won European competition, played Champions League semi-final.
"This guy is much cheaper than a young English lad. And he is good for our average wages.
"Sometimes you have to make decisions. I don't criticise the other clubs for paying it. They can pay what they want.
"I don't have any comment about it. But for my club, we can say it would be very negative for us."
Meanwhile, United boss Louis van Gaal has admitted he plans to speak to Mourinho over his claims about the Shaw deal.
"I don't think I have to discuss things in the media, it's better to discuss it with Jose," he said.