Mourinho is under pressure following consecutive Premier League defeats to Brighton and Tottenham, with speculation mounting about his future at the club.
The United manager demanded respect from journalists following the 3-0 loss to Tottenham, pointing to his success with Chelsea, Inter Milan and Real Madrid.
Guardiola was involved in a series of spats with Mourinho when he was in charge of Barcelona.
But, asked about Mourinho’s problems, Manchester City boss Guardiola said: “The history, the way Jose did in all the places he was – it’s hat’s off. There is no doubts about his quality.
“You need players, good clubs that sustain you and support you, patience.
“Our position is results. Every manager what he believes, what he likes, tries to get results in his own style and the way he trains. We are judged on the results we get.
“Only the players know exactly how you are as a manager because they know you and see you every day. They have more information than the rest of the world – the fans, the media, everybody.
“Only the players know exactly who we are and normally even then we are judged – if they play, the manager is good, if they don’t play the manager is not good.”
– Magic Mahrez –
Meanwhile, Guardiola has spoken glowingly of pre-season signing Riyad Mahrez.
The Algeria winger joined City from Leicester for a club record £60 million ($77 million) and has settled well, according to his manager.
“He is one of the most technical players I’ve ever seen, the skills and everything,” Guardiola said.
“Of course there’s a lot of information – the way we want to play, the way we want to do things, the corrections after the games that we have to do, in all things, defensive and offensive set-pieces.
“But he settled good. He has respect in the locker room and that is the most important thing.”
Speaking ahead of City’s weekend Premier League clash with Newcastle, Guardiola appeared relaxed about the challenge of winning back-to-back titles.
Asked if this season will pose of tougher challenge for the champions, he said: “It will be quite similar, I would say.
“New managers are here – Marco Silva at Everton, Maurizio Sarri at Chelsea – new managers, new clubs. Javi Gracia at Watford is doing amazingly. But I think it’s too early.
“Last season we cannot forget all the six contenders playing international competitions, not like the previous season when Chelsea didn’t play there. It was tough last season, it will be tough this one.”
Guardiola believes his squad is up to the job and he is happy with performance levels in the opening weeks of the new campaign, with two wins before last weekend’s surprise draw at promoted Wolves.
“They are doing a fantastic job all of them. They convince me when they put everything on the pitch. I am a romantic guy,” he said.
“Who runs the most, I am the happiest guy in the world and I appreciate it a lot.
“I want to be sure when one guy is on the pitch, he gives everything. Run, you are my favourite one. They do it most of the time.
“Normally, when one player plays good, it’s for many reasons, not just because he played good himself.
“Their team-mates, the way they receive the balls, helps them to play better. It’s all together, not just one.”