United are just a few games a way from securing a second spot finish in the Premier League this season, but Mourinho's style of play has been heavily criticised in recent weeks after a string of weaker performances.
In a panel discussion on 'The Debate', Bellamy said: ''With United, they're used to winning trophies. And of course, he'll look and say I've done it but the league is what it's about. That's their identity. Their history is incredible.''
He noted that after the retirement of Sir Alex Ferguson in 2013, the club had failed to claw their way back to the very top of the league and Mourinho's appointment was a last-ditch attempt to turn their luck around.
Bellamy added: ''I believe their desperation to get back on top, to the top of the league, is why they went for Mourinho. They said forget about the identity, don't worry about what's gone on before, this is what we need right now, just get us there.''
''I'm not going to sit here and say Mourinho isn't a brilliant manager, of course he is, but in my own terms he's not a Manchester United manager - what I'm used to, what I've watched this great club produce, their identity and how they play, how they've stuck to it down the years.''
He added: ''United have had so many great teams over the years and look at this team - it doesn't even compare. In my era, Scholes, Keane, Giggs. I know football has changed, but it was always quick football with United back then. It's a lot slower now.''
The former Wales international concluded: ''Man United fans will be looking at it thinking: 'We need to be better.' But if they do win the FA Cup it'll be three trophies in two years, and that's not a bad result.''