Payet, 29, did not train with the first team in January after Hammers boss Slaven Bilic said the Frenchman no longer wanted to play for the club.
West Ham rejected two bids from Marseille for the player, but decided to sell him on 29 January after signing Robert Snodgrass from Hull City for £10.2m.
In a statement on the Hammers website, Sullivan said the club had decided to sell Payet in the "interests of squad unity".
"The club would like to place on record its sincere disappointment that Dimitri Payet did not show the same commitment and respect to West Ham United that the club and fans showed him, particularly when it rewarded him with a lucrative new five-and-half-year deal only last year," he stated.
"I would like to make it clear that we have no financial need to sell our best players and that the decision to allow Payet to leave was in accordance with the wishes of the manager and the interests of squad unity.
"To be frank, my board and I would have preferred for him to have stayed in order to make an example of him, as no player is bigger than the club."
Payet joined West Ham from Marseille in 2015 for a fee of €11m. He made 60 appearances for the club, scoring 15 goals.
Sky Sports said that the Frenchman has taken a £25,000-a-week pay-cut to move back to Marseille, with the Hammers imposing a 25% sell-on clause on his transfer deal.
Sullivan added: "I am confident that with the quality of the players we have brought in during January already, the squad will be stronger at the end of this transfer window than it was at the start.
"We now look forward to building on our recent good run of form with five league wins in the last seven matches as we focus on continuing our rise up the Premier League table."