The Blues announced the €30 million signing of Pedro on Thursday, having capitalised on United's unwillingness to match Barcelona's asking price with a late bid for the unsettled winger.
United have since moved to distance themselves from suggestions of another public humiliation in the transfer market for executive vice chairman Ed Woodward, with boss Louis van Gaal on Friday claiming that the media exaggerated his level of interest in signing Pedro.
But Antonio Sanz insists it was United's indecision that cost them dearly in pursuit of the 28-year-old, comparing the speed of discussions with Chelsea to a "whirlwind".
"Maybe Manchester United fell asleep," Sanz told Radio Club Tenerife. "The negotiation with Chelsea was like a lightning bolt.
""It is common knowledge that United were in the bidding for Pedro, but Chelsea were faster and within 24 hours reached an agreement with the club. It was a whirlwind."
At his Friday press conference Jose Mourinho hailed Pedro as "one of the best attacking players in the world" and Sanz has no doubt that his agency's client will shine in England.
"Pedro is going to have a very good year and is going to be one of the sensations of the Premier League," he declared.