Shaw - a boyhood fan of the London club - had been in a tug-of-war between Premier League rivals Chelsea and Manchester United for much of the close-season before making the move to Old Trafford from Southampton in a big-money deal.
Mourinho eventually opted for cheaper alternative Atletico Madrid full-back Filipe Luis, claiming the 19-year-old England international's arrival would have "killed" the club due to UEFA's Financial Fair Play rules.
The Portuguese boss also highlighted the unrest Shaw's transfer would have caused within the dressing room at Stamford Bridge.
"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."
Mourinho added: "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."
