The 47-year-old Uruguayan was sacked on Monday in the wake of a horrendous 4-0 home defeat by Aston Villa which left the club perched just a point above the Barclays Premier League relegation zone.
But on the day his successor Dick Advocaat met the media for the first time, Poyet insisted he left the Stadium of Light after 18 months at the helm with his head held high.
He said in a statement released on his behalf by 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 Barclays 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 short-listed for the Barclays 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.
"Of the three Tyne-Wear derby matches since I joined the club as manager, I am very proud that we were able to win all three, two of which were away from home."
Poyet was appointed in an attempt to bring stability to the club after Paolo di Canio's brief, but tempestuous reign, and while he was disappointed to lose his job, he thanked chairman Ellis Short for giving him his chance in the top flight.
He said: "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 also thank my staff for their valuable assistance, the players for all their efforts and, in particular, the fans, who demonstrate such unbelievable passion for the club.
"I sincerely wish everyone connected with Sunderland the very best for the remainder of the season and beyond."