He also revealed that the failed experiment of hiring a director of football and a big-name manager directly resulted in West Ham's decision to go back to British by re-hiring David Moyes as Pellegrini's successor.
Chilean former Man City boss Pellegrini was appointed in May 2018 as West Ham fans pleaded for a successful head coach with a big reputation, and supporters also got their wish as a director of football swiftly followed to the London Stadium.
Mario Husillos was the man selected to become West Ham's first official director of football, and he oversaw the arrivals of a host of new players during the summer 2018 transfer window.
Jack Wilshere, Andriy Yarmolenki, Fabian Balbuena, Felipe Anderson, Lucas Perez, Carlos Sanchez, Xande Silva, Issa Diop, Lukasz Fabianski and Ryan Fredericks all arrived at the London Stadium that summer, with Samir Nasri following in December, as the Hammers spent over £170m during Pellegrini and Husillos' spell at the club.
While finishing 10th in the 2018/19 campaign promised a bright future, Pellegrini was sacked in December 2019 - with Husillos following him out the exit door - and Moyes returned to the Hammers once again.
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And Sullivan believes the failed experiment proved West Ham were right to return to a manager in total control of footballing matters, rather than allowing a head coach to be influenced by others - including co-owner Sullivan himself!
Speaking to White and Jordan on talkSPORT, Sullivan revealed: "Under the previous regime, the only two players I picked were [Issa] Diop and [Lukasz] Fabianski; I bullied the manager to take them because I liked both players.
"All the other players him and his director of football picked and I regret in a way not stopping some of the signings, because you have to back the manager.
"We chased dreams over the past few years and bought a pile of players who unfortunately haven't improved the club; maybe they will over the coming seasons because there are some damned good players.
"I left it to the previous regime for two years and they didn't buy well.
"The fans were on my back to have a director of football, a big-name manager. We did what the fans wanted - it didn't work.
"We have now gone back to grassroots, a British manager. He is picking his players. The final decision is the manager. "
Listen to David Sullivan on talkSPORT, above…
West Ham co-owner David Sullivan admits he regrets not BLOCKING signings made during Manuel Pellegrini's reign as manager.