But Mourinho, who also criticised the performances of several Chelsea players and himself, refused to gloat at having apparently put one over rivals Manchester United, who had been regarded as favourites to secure his signature.
"I only want to beat Manchester United on the pitch," the Portuguese told a news conference. "I don't want to say we won, that's not the point."
He is nevertheless delighted to have given Chelsea an extra attacking option and has already been impressed with Pedro's attitude.
"He wants something more for his career, that's an evident sign of ambition.
"He won everything playing with all these stars but he wants more and I'm really happy with that.
"When I'm told a player wants to leave Barcelona or Real Madrid, these giant clubs, I always ask 'why?'
"He loves Iniesta, Messi, Neymar and those guys but will leave the comfort zone and come here to a new club, new country, new culture."
Signing Pedro and the Ghana international Baba Rahman, a left-back, from Bundesliga club Augsburg has given Chelsea a boost after a sluggish start in defence of their Premier League title.
They drew 2-2 at home to Swansea after goalkeeper Thibaut Courtois was sent off, and then lost 3-0 to Manchester City.
"We are not happy (with results) but we are calm," Mourinho said. "This week we got a very good young left-back and we got one of the best attacking players in the world."
However, the Portuguese coach later said he was not happy with the form of several players and named them.
"I'm not happy with anyone," said Mourinho. "I'm not happy with Branislav Ivanovic's form, Gary Cahill, John Terry, Cesar Azpilicueta, Eden Hazard, Cesc Fabregas, Nemanja Matic."
"I'm not happy with my form because I used to get better results than I'm getting now."
On Sunday Chelsea visit Tony Pulis's West Bromwich Albion, hoping to avoid another addition to a bizarre run in which their last half dozen league defeats have all come from managers beginning with the letter P - City's Manuel Pellegrini, Pulis at West Bromwich and Crystal Palace, Tottenham's Mauricio Pochettino, Newcastle's Alan Pardew and Sunderland's Gus Poyet.
Mourinho claimed not to be aware of that run but smilingly added one of his own for those of a superstitious bent: after previously starting the season with a 2-2 draw, at Porto and Inter, he went on to win the treble.
(Reporting by Steve Tongue, editing by Pritha Sarkar and Ken Ferris)
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