The Manchester United defender aggravated a thigh injury on international duty against Germany, with it later emerging that the 25-year-old had been given six injections of local anasthetic in order to be able to feature in the game.
As a result of the injury, Jones missed United's win over Newcastle at the weekend and remains sidelined, leading to criticism from Mourinho.
Speaking on 'The Debate' on 'Sky Sports', former Arsenal striker Wright says that it is ridiculous that Jones would take six injections to play in a friendly.
"I think the doctors have got to take more responsibility, rather than giving a player of that calibre and a club of Manchester United's size, to get in touch and say something…That is something that has got to be discussed between them, instead of him taking six injections to play in a friendly," he raged.
"I did it in the cup final in 1994. I took three, then another three for the replay, in a week, but not in one sitting. That was bad enough, that's why I'm walking around now with a fused ankle. But at the same time I wanted to play in that final. Phil Jones has got to say, 'for a friendly?'
"He [Mourinho] looked like he was seething and he should be."
Wright was backed up by former Arsenal and England team-mate Paul Merson, who said Jones should have taken more responsability and refused to play.
"Surely he is big enough and old enough, he's playing for one of the biggest clubs in the world, and he has been around a while, surely he is old enough to say 'I can't have six injections, this is a friendly'," said Merson.
"I don't think you can blame the doctors. I have had injections before and the player has got to have agreed and said I want to play.
"Gareth [Southgate, England manager] was saying a month ago that Phil Jones is one of his main England centre-halves. If that's the case why does he have to have six injections for a friendly?
"I can understand if it's someone like Ruben Loftus-Cheek who is just getting in and is going to make their debut and trying to get to the World Cup, but Gareth is saying he is one of his top centre-halves and he's having six injections."