Lampard was expected to link up with new MLS franchise New York City - the sister club of the Premier League champions - ahead of the start of the US domestic season in March but he will now stay in England.
A deal has been agreed for him to remain with Manchester City until the end of the top-flight campaign, following an initial short-term spell.
As a result, Lampard will now not head to the US until July, much to the frustration of New York's supporters.
In an interview with Sports Illustrated, Garber said: "I could understand why their fans [New York] are unhappy, and I do believe [the club] will work hard to build back that trust.
"They've started that process already. I sensed this was coming, and it didn't surprise me when they ultimately made their decision. You're dealing with a very unusual set of circumstances.
"Frank has become one of the most important players in Man City's season, and he’s scored critical goals to have them tied for first place in the Premier League. They were faced with a difficult decision."
A number of big-name players have previously moved to MLS in July at the end of the European domestic season, and Garber feels there would have been less uproar had an initial announcement not been made regarding the timing of Lampard's arrival.
"I'm going to be supportive of all our ownership groups, making them aware of my point of view. But we need to work hard now to move forward and recognise that Frank will be joining this team in July along with other designated players, who throughout the history of the designated player programme have almost always joined in July.
"If there was an error in judgment on this, it was not just announcing that he would come in July and figuring out how to manage the start of the season, no different than what happened with Robbie Keane or Thierry Henry or David Beckham.
"I think it's important to say this: These guys [the owners of New York City] are very committed to MLS and committed to New York. They have made an unprecedented investment in MLS and New York City, and they are going to continue to do so.
"This kind of decision is not something in my view that in any way says this [New York] is a farm team for Man City. I don't believe in all my dealings with them that they have led us to believe that's true."
Garber also commented on the future of Steven Gerrard, who has indicated he is close to sealing a move to MLS after choosing to leave Liverpool when his contract expires at the end of the Premier League season.
"Discussions are taking place with his representatives, and we expect more details soon. I can't say anything further than that. Nothing is signed," Garber added.
