The Reds were desperate to sign the Dutchman and pursued him throughout the transfer window.
But despite Van Dijk handing in a transfer request, the Saints refused to do business.
Le Tissier has hailed his former club for holding their nerve and says it was the right call.
“I thought they handled it excellently, I really do,” he said on Sky Sports.
“Right from the start at the end of last season, they said ‘we are not interested in selling our players, we’re not interested’.
“Again, the length of contract was key for me.