Saints chairman gets firm on any more transfers
Rickie Lambert, Luke Shaw, Adam Lallana, Calum Chambers and Dejan Lovren have all departed the Saints since their eighth-place finish in the 2013-14 Premier League.
And with Tottenham - managed by former boss Mauricio Pochettino - looming for the services of Morgan Schneiderlin and Jay Rodriguez, Kreuger said he has had enough of his players jumping ship after such a promising league campaign.
While Kreuger admitted disillusioned players had to be let go to maintain a positive team culture, he said manager Ronald Koeman also needed the likes of Schneiderlin and Rodriguez to build around.
"You cannot begin a Premier League season with half of your starters disgruntled," he said.
"That was clear to us so we needed to be willing, if a premium was hit, to let players go. We got our premium but we came to a clear conclusion that Morgan and Jay were not going to be sold.
"It's clear that certain players when Ronald came in were flagged as potential core players long term, within their positions."
Schneiderlin tweeted his disappointment with Southampton after meeting with the club last week, claiming his relationship with the coastal club had been "destroyed".
But Kreuger neglected to hit out at the France midfielder, and also reiterated his belief the £10 million offer from Spurs was insufficient.
"I don't take anything personally," Krueger said, in relation to Schneiderlin's tweet.
"We are dealing with human beings. People are communicating with different styles now.
"You will have these kind of situations all through the season. You will never have 25 players going, 'Yeah I love everybody here'.
"But when I sign a contract, the understanding I have is that I have to be prepared to fulfil that contract and anything else that develops needs to be a win-win situation.
"It was a win-win on those other [transfer] situations for both sides."