Poyet was dismissed on Monday, leaving Sunderland again embroiled in a battle to safeguard their top-flight status, with Dick Advocaat replacing him at the Stadium of Light initially until the end of the campaign.
That Sunderland are still a Premier League club at all is down to Poyet inspiring a late upturn last term that included wins at Chelsea and Manchester United and a 2-2 draw at Manchester City to haul themselves out of the mire.
It remains an achievement that the Uruguayan – who also steered Sunderland to the 2014 League Cup final – holds in high regard.
Poyet said in a statement realised via the League Managers' Association: "Certainly I am very disappointed to have left Sunderland, but I am extremely honoured to have served this special club as their manager.
"When I arrived in October 2013, Sunderland had played seven matches and lost six, gaining only one point and they were bottom of the Premier League.
"Thirty one matches later, at the end of the season, we had won 10 and drawn eight, taking us to the complete safety of 14th position.
"I will always remember fondly that miracle unbeaten run, a vein of form for which I was honoured to be shortlisted for the Premier League Manager of the Year Award.
"I leave Sunderland feeling proud of all of our achievements during my tenure, not least reaching the club's first cup final in 22 years when we took more than 30,000 fans to the Capital One Cup Final at Wembley.
"I would like to take this opportunity to thank chairman Ellis Short for giving me my first opportunity to manage in the Barclays Premier League, without a doubt the greatest league in the world.
"I sincerely wish everyone connected with Sunderland the very best for the remainder of the season and beyond."
Sunderland are one point above the relegation zone and Advocaat's tenure begins with Saturday's trip to West Ham.
