According to statements released on West Ham's official website, co-chairman David Sullivan voiced his disappointment after the Frenchman moved to the French side for $32 million, reports Efe.
"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," Sullivan said.
He clarified that the English club has no financial need to sell its best players, adding that the decision to allow the French player to leave was taken "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," Sullivan reiterated, according to the website.
Payet, 29, joined West Ham in June 2015 from Marseille for $13.3 million, scoring 12 goals in his first season and named by the Professional Footballers' Association as player of the year.
Sullivan stressed that he is "confident" that his club will be stronger with the quality of the players brought in January.
"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," he concluded.
West Ham signed defender Jose Fonte from Southampton and midfielder Robert Snodgrass from Hull City this January to strengthen the team.