Lampard came off the bench to score a 73rd-minute winner in the New Year's Day game, hours after City confirmed that he will remain at the club until the end of the season.
City officials claimed that Lampard has been loaned to the club from Major League Soccer franchise New York City FC, City's sister club, who he signed for after leaving Chelsea at the end of last season.
He had initially been due to join up with the American outfit on January 1.
But it emerged that Lampard has not signed a loan deal with the defending Premier League champions, but has in fact signed an extension to the short-term contract that saw him join Manuel Pellegrini's squad in August.
It calls into question the exact nature of Lampard's contract with New York City and when asked whether the 36-year-old midfielder would ever play for the MLS side, City manager Pellegrini refused to answer.
"We are only finishing December," the Chilean said in response to the question
"I think you can't have all different questions about Frank Lampard.
"Frank Lampard will stay now with us until the end of the season
In the month of May, you can start thinking about what will happen in the future."
New York City supporters have been vocal in their dissatisfaction with City's handling of the Lampard affair, even though their club have yet to play a game.
A statement from supporters' group the Third Rail claimed that Mansour bin Zayed Al Nayhan, who owns both clubs, was treating the New York version as an inferior member of his football stable.
- Poyet admires City cunning -
But Pellegrini said that even if City were to exit the Champions League knock-out stages early, there is no possibility of Lampard making a move across the Atlantic before May.
"That's why, every time you asked me what was happening about Frank Lampard in December, I repeated that we were trying to keep Frank, but it was not easy because other people, other cubs were involved in this situation," he said.
"I understand perfectly New York fans want to see Frank playing because for the fans to see Frank Lampard playing in New York City is amazing.
"I hope he will be there next year, but I think at this moment it is the best decision for him, for the club, for New York, for him to stay here with us until the end of the season."
Lampard scored a dramatic winning goal, his fifth of the league season, three minutes after coming on against Sunderland after his side had squandered a lead handed to them by Yaya Toure and Stevan Jovetic.
Former City players Jack Rodwell and Adam Johnson, with a penalty, equalised for Sunderland before Lampard's winner.
With former leaders Chelsea subsequently losing 5-3 at Tottenham Hotspur, it left City neck-and-neck with Jose Mourinho's side at the summit.
Meanwhile, beaten manager Gus Poyet refused to condemn City for their handling of the Lampard issue and said they deserved credit for the manner in which they had used the regulations to sign the former Chelsea star.
"For me it's clever, it's smart," said the former Chelsea midfielder
"It's legal, so I've got no problem with that
But his goal? Yes, I do have a problem with that!
"That's more something I can control
When you're playing away at the champions and you find yourself 2-0 down, you need to do something very special to come back, so after coming back we needed to do better.
"It's Frank Lampard, we know what he does
He's going to arrive late in the box so we need to mark (him)."
Source : AFP
Source: AFP