The 19-year-old joined Manchester United for £30 million in June, with the club making him the highest-paid teenager in the world with a £160,000-a-week salary.
Goal understands Chelsea pulled out of the race to sign Shaw when they became aware of the wages on offer from United, with Mourinho adding that such a salary would have angered other squad members.
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"Because when you pay that much to a 19-year-old kid - a good player, fantastic player - but when you pay that amount of money, the next day we would have had players knocking on our door.
"They would have been saying 'How is it possible I play 200 games for this club, won this and that, yet a 19-year-old comes here and gets more money than I get?'
"It would've killed immediately our balance, and we couldn't allow that."
With Ashley Cole leaving the squad following the expiry of his contract, Chelsea moved quickly to sign Filipe Luis from Atletico Madrid for around £16 million - a deal Mourinho feels represents better value for money.
He continued: "I don't criticise another club 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, especially when we can say Felipe is much less expensive.
"Filipe played for Brazil, won titles in Spain, won European competitions, played in the Champions League final. Yet this guy is much cheaper than an English young lad.
"And is he good for our average wages? Yes he is. Sometimes you have to make decisions."