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The former Barcelona forward completed his move to London, having been at the centre of a long-running transfer saga involving United over recent weeks.
While Old Trafford boss Louis van Gaal denied he had directly expressed interest in the 28-year-old, Mourinho was quizzed about whether it was an off-field victory for Chelsea.
But the Portuguese, whose squad has also been bolstered recently by left-back Baba Rahman, said: “I only want to beat Manchester United Nike Women Hypervenom Cleats on the pitch if possible. I don’t want to go in that direction.
“Our job here is not to try get player another club wants. It’s to get players we think are good for us. The market is an opportunity window where you have to be careful not to lose best players but you can also get players you are not expecting to get.
“In this case I don’t want to say we won or lost, that Manchester United wanted or didn’t want him. Pedro is a player we like a lot and we are happy to have him.
“For me everything started Nike Women Magista Cleats with the fact that finally we understood that the player was ready to leave the club Nike Women Soccer Cleats of his dreams, the club of his heart, where he played since he was a kid and where he won everything.
“When I’m told a player wants to leave Barcelona, Real Madrid, these giant clubs I always put a question mark. Why do they want to leave? Normally it is rumours that are never true. It was true.
“He has amazing respect, he loves [Andres] Iniesta and [Lionel] Messi and Neymar – these guys he’s played with but everything he does he would always be behind.
“It’s time to enjoy a different challenge, leave the comfort zone to a new club and country so I’m happy with his approach.”
Pedro’s arrival also prompted further debate over Juan Cuadrado’s future, the Colombian having struggled to establish himself at Stamford Bridge since his move in February.
“Some questions you ask me Adidas Women Soccer Cleats that are unique,” Mourinho continued.
“Nobody ask [Manchester City boss Manuel] Pellegrini about [Vincent] Kompany after Nicolas Otamendi’s arrival. Nobody ask about [Martin] Demichelis or [Elaquim] Mangala.
“It’s natural, they buy a Nike Women Mercurial Cleats centre-back. They have four but this is a question that comes only to me.
“So, I also read about Mr Van Gaal having 28 players and being happy. With Pedro we have 23, so let us be calm and see what happens.”