City confirmed on the eve of the game that Lampard's stay at the Etihad Stadium had been extended until the end of the season, having initially been set to expire at the turn of the year at which point the midfielder had been due to join MLS side New York City - owned by the English champions.
And the move worked perfectly in the hosts favour as Lampard emerged from the bench to seal a frantic 3-2 Premier League victory.
Goals from Jack Rodwell and Adam Johnson had cancelled out Yaya Toure's stunning effort from distance and Stevan Jovetic's flick, before the 36-year-old settled matters in a breathless 16-minute spell.
Lampard's extended stay with City has caused some consternation in the United States in particular, but Poyet sees no issue.
He said: "It was looking to me last week like it was not possible but by the end it was possible. How, I don't know. I'm not an expert on the rules and regulations.
"But he made a difference today by scoring the winning goal.
"For me it's clever. It's legal so I don't have a problem with that."
Sunderland's fightback from two goals down evoked memories of last season's 2-2 draw in the corresponding fixture as Poyet's side launched an unlikely survival from the drop.
Though delighted with the spirit shown by his side in pegging the champions back, the Uruguayan was left disappointed by their failure to see out the job.
He added: "When you're playing away against the champions and you find yourself 2-0 down you need to do something very special to come back.
"And after coming back we needed to do better. The disappointing side of the performance today is after the 2-2. The last 15 minutes we gave the goal away too easily.
"We made it difficult and I think that they were getting to the point of frustration and then with the change you have more options on the break and fresh legs and then he [Lampard] scores because he does things that no one else can."
