Lampard initially joined City on loan for six months from New York City FC after leaving Chelsea at the end of last season.
But the deal with the English club, who are currently second in the Premier League, has been extended till May or June, which means the 36-year-old could miss the first three months of the MLS season.
"We would like to publicly denounce... Frank Lampard’s decision to extend his loan to Manchester City until the end of the Premier League season," New York fans group the Third Rail said in a statement.
"Many fans, including our members, decided to support the team, committed to season tickets, and bought merchandise under the impression that Frank Lampard would be playing for New York City Football Club, not Manchester City."
"Many of those fans are rightly outraged by this decision, and we support any course of action they take to voice their discontent over this decision.
"We reject out of hand any suggestion that NYCFC is in any way secondary to Manchester City FC, regardless of the source, and are disappointed that City Football Group would give such an appearance."
New York City are owned jointly by Manchester City and baseball giants New York Yankees and will play at Yankee Stadium when the 2015 MLS season gets underway in March.
The 36-year-old Lampard has scored six goals for City this season and his starting date at with New York will depend on the club's results this season.
The Premier League ends on May 24, while the Champions League final takes place on June 6. Manchester City face Barcelona in the last 16 next month.
(Writing by Pritha Sarkar in London, editing by Amlan Chakraborty)
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