The former Arsenal goalkeeper, angry at Mourinho's recent remarks about Arsene Wenger being "a specialist in failure", also described Mourinho's comments as "disrespectful" and "despicable".
And the 72-year-old told BBC Five Live's Sportsweek programme that "boring" Mourinho should behave like the "gent" Sir Tom Finney, who died on Friday aged 91, rather than continue to attack the Arsenal manager who is "a genuinely good guy and a footballing man".
Mourinho made his "specialist in failure" comment on Friday in response to Wenger's claims that the Premier League title is Chelsea's to lose.
Mourinho has repeatedly played down Chelsea's chances of winning the Premier League this season, declaring his side are third favourites behind Manchester City and the Gunners, despite being leaders with 12 games remaining.
"He is a specialist in failure. I'm not," said Mourinho, whose side lost 2-0 to Manchester City in the FA Cup fifth round on Saturday.
"If supposedly he is right and I'm afraid to fail, it's because I haven't failed many times."
When asked about the comments, Wilson said: "I think at best it was disrespectful, at worst despicable to be so dismissive of a genuinely good guy and a footballing man I think, whose presence in England in 17-18 years has opened eyes and ears and created wonderfully entertaining sides.
"It's obviously not the first time Mourinho has singled Arsene out. He called him a voyeur which is a disgusting claim and thankfully on that occasion he - although belatedly - he did apologise.
"I think it's personal, he is hugely talented, amazing manager Mourinho but I find - at this moment - I find him boring at the moment.
"To call (City boss Manuel) Pellgrini the abuse that he's called him to do with Arsene, this is a weekend when we honour a gent - Tom Finney, Sir Tom, and I don't like bullies."
Wilson, who spent his professional career at Arsenal from 1963 to 1974, admitted he endured some banter from former Liverpool boss Bill Shankly when he was at the Gunners, but it was said in good spirit.
He added: "I like people who have within them some humility as well.
"I think I heard the name (Bill) Shankly in there. Shanks was in a way, in his day like Jose Mourinho.
"It was every opportunity to just psyche you out or to come out with things.
"On a personal basis, I came out of Loughborough University and I got thrown into the Arsenal first team and I was putting tickets on the door when he took one look at me, knew exactly that I was an amateur school teacher and went to the Arsenal official there, (and said) 'Are Arsenal at full-strength tonight or is that Bob Wilson playing?'
"And in 1971, the day before we played in the (FA Cup) final against Liverpool, he was the only guy in the (Wembley) stadium as we looked at it and as we went by, (the lads said) 'See you tomorrow Mr Shankly', (he said) 'Aye, good luck son'.
"As I went past and I said 'See you tomorrow Mr Shankly', he said, 'Aye, Bob. Nightmare pitch for goalkeepers eh?'
"And he was getting at you, but he was getting at you in a really lovely sort of competitive way."
Earlier this week, Mourinho also caused a stir with City boss Pellegrini ahead of Saturday's FA Cup tie.
Chelsea have twice beaten City in the league this season and the Blues manager had experienced defeat against Pellegrini just once in nine meetings in Spain and England before the 2-0 result - which sent City into the quarter-finals.
Pellegrini recently stated he did not wish to talk about Mourinho, who insisted he would prefer not to talk about his counterparts.
Mourinho said on Friday: "If he (Pellegrini) doesn't like to speak about me, perfect. And I hope he does what he says.
"I also don't like a lot to speak about other managers."
Lord Sebastian Coe spoke out in defence of the Chelsea manager, stating he is only merely answering the questions put to him by the media.
The Team GB boss told Sportsweek: "This is an interesting contradiction.
"All he's doing is answering the questions that he gets asked. The manager appears before the press before a Premier League or Champions League game...he gets asked the questions.
"I'm not sure these are mind games, I know they're not mind games.
"He's answering the questions he's being asked and he's actually doing it with honesty."
When quizzed on his banter with former rival Steve Ovett, who also represented Great Britain in middle-distance running - winning 800m gold in the 1980 Moscow Olympics - Coe made it clear they would not air their views publicly ahead of a race.
He said: "I think we were both acutely conscious that anything we did.
"You could probably count the number of direct quotes that ever came out from either of us about each other on the fingers of one hand.
"We were just acutely conscious, it didn't really matter what we said it would get taken out of context.
"If you'd asked me at the time 'Did you think about him', and the standard answer was 'No', he'd probably say 'We were focused on what we were doing'."