Pedro Rodriguez's agent says Manchester United "probably dropped the ball" in the battle for the Spain star and that Chelsea's swoop was more "like a lightning bolt."
Chelsea, in a bid to recover from their worst start to a season in 17 years, signed the 28-year-old Spain forward on a four-year deal on Thursday after weeks of discussions to move to United.
Pedro, who cost €30 million (£21.4 million), with €3 million in add-ons, trained with his new teammates immediately and could make his debut against West Bromwich Albion on Sunday.
His agent Antonio Sanz told Radio Club Tenerife that United offered the exact same money but in a different breakdown.
"It is well known that Manchester was in the race for Pedro but Chelsea were faster and in 24 hours they reached an agreement with the club," the agent said.
"It took them a little while longer [to reach the agreement with the agency] with us, but essentially it was as fast as a lightning bolt.
"These are things you have to get done on the fly. The opportunity that was given to Chelsea was there to take advantage of."
Sanz added that "any change requires an adaptation period, but language would not be a problem because the language of football is universal.
"Pedro is going to shine this year and is going to be one of the biggest sensations in the Premier," Sanz said.
Sanz also confirmed that Chelsea coach Jose Mourinho had reached out to Cesc Fabregas but reminded fans that at the end of the day it was Chelsea's decision.
"When a coach calls you it makes you think that you are going to be important," Sanz said.
Sanz said he felt Pedro would debut against West Brom.
"That a Spanish player is sold for that much money corroborates the fact that he was a very important player in Barcelona's history," he said.