The newest addition at Stamford Bridge was widely expected to join the Red Devils before a frantic 24 hours ended with the Spaniard signing in London.
It was reported persuasion from Mourinho and Pedro's former Barcelona team-mate convinced the 28-year-old to move to the Blues instead of joining Louis van Gaal at Old Trafford.
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But the Portuguese boss has claimed there is only one place he cares about beating Manchester United.
As per the BBC, Mourinho said: "I only want to beat Man United on the pitch, I don't want to go in that direction. Our job is not to get a player another club wants."
Pedro joined Chelsea in a £21.4 million deal and is expected to make his debut at West Bromwich Albion on Saturday, along with Abdul Baba Rahman, who also joined the Blues this week from German side Augsburg.
MORE TO COME
Chelsea have sprung into action since their 3-0 defeat at Manchester City and have also lodged a bid for Monaco's 19-year-old forward Anthony Martial.
Mourinho also refused to rule out more signings before the transfer window closes, stating their was always an opportunity.
The 52-year-old said: "While the transfer window is open, it's the opportunity window, we have a very good young left-back with potential and have one of the best attacking players in the world."
In recent days the odds on Paul Pogba to join Chelsea have been dramatically slashed leading to speculation the former Manchester United man could be on his way to Stamford Bridge.
TRANSFERS WERE NEEDED
After a poor start to the season it was imperative for the defending Champions that they strengthened their squad. Despite winning the title in comfortable fashion last season, it is always important to improve the playing squad and make sure the feeling around the club does not go stale.
The additions of Pedro and Rahman bring added quality and pace to the Chelsea team, another couple of signings in the forward and midfield positions would give Mourinho's side the perfect platform to turn around their lacklustre start to the season.