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."
The comments from the Chelsea supporters on here say all that you need to know, really. Blue, in particular, who does not know who Bob Wilson is but claims to be a football supporter. These Chelsea supporters must not have a very high opinion of themselves, which has been evident many times, if they are happy to see their manager call someone as successful as Wenger 'a failure'. Wonder what Jose thinks about them?- Gab1965