Suarez scored twice in his country's crucial 2-1 Group D victory over Roy Hodgson's side in Sao Paulo in his first game back after injury.
The Liverpool striker underwent minor knee surgery just four weeks ago, but still proved to be too lively for England's defenders to handle on Thursday despite clearly not being 100 per cent fit.
Suarez came into the World Cup on the back of a superb campaign at club level, with his haul of 31 Premier League goals leading Liverpool's unlikely title challenge.
His performances resulted in him sweeping the board in English football's end-of-season individual awards, and appeared to draw a line under his past indiscretions.
And Chelsea manager Mourinho - whose side finished third in the Premier League, one place below Liverpool - believes a more mature Suarez is one of the world's best players when he lets his talent do the talking.
"I think there are two periods of Luis Suarez," the Portuguese told Yahoo.
"The one period, before I arrived (back at Chelsea in 2013) he had bad behaviour. Obviously he was criticised.
"After that there is a second period of Suarez, which was this last season and this season he was voted by the English football press association as the player of the season, so I think they all recognise that he is a fantastic player.
"When his behaviour is okay, people give him the credit he deserves.
"I speak by myself - when he dives and tries to win penalties out of nothing I don't like the situation.
"But when he plays like he did many, many times for Liverpool, and when he plays like he did (against England) - I have to say, (he is) absolutely amazing.
"The commitment, the connection with the players, the connection with the supporters - I have to say, amazing."
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
