The Foxes were confirmed as champions after Tottenham failed to beat Chelsea at Stamford Bridge on Monday, despite starting the campaign as 5000/1 underdogs.
Leicester's rise to supremacy included a 2-1 victory over West Ham at Upton Park and a 2-2 draw in the reverse fixture, though the Hammers chief seemed considerably less impressed than others when asked about their success.
“I know how they've done it," Sullivan told Sky Sports.
"They've got 11 penalties, lady luck shined on them. They've had virtually no injuries. They've only used 18 players all season.
“They've had two players who've played out of their skin, scored more goals than they've ever scored in their entire lives.
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“They signed a fantastic midfielder. One of their big signings came good, and that's how they've done it. You don't see them being massively better than you [West Ham] are.”
The 67-year-old also believes that the performances of Manuel Pellegrini's City and London rivals Spurs were more deserving of the Premier League crown, despite the eventual winners.
“In contrast, Man City and Tottenham on a good day are real good teams, better than Leicester. The table doesn't lie and Leicester are the champions.