Phil Jackson said Carmelo Anthony took less than the maximum $129 million contract, and the Zen Master declared he needs his star player to maximize his teammates to win a championship.

Anthony officially announced he was coming back on his website early Sunday afternoon, writing an essay with the headline “My Heart, My City.’’ Anthony wrote: “I am a New York Knick at heart.’’

Anthony took less to stay with the Knicks — estimated at $122 million to $123 million over five years. But it was still a lot more than what the cap space-challenged runner-up Bulls could offer — four years, $73 million.

Jackson confirmed The Post’s reports Anthony structured the deal to give the Knicks more cap space in 2015. It is believed he didn’t take his annual 7.5 percent raise in Year 2 and may have taken a tiny pay decrease. Under collective bargaining agreement rules, a player can receive as high as a 7.5 percent pay raise annually.

“He did exactly what we kind of asked him to do,’’ Jackson said. “Give us a break in the early part of the contract when we have some wiggle room — hopefully big enough wiggle room — next year when we can exploit it.’’

Anthony’s sacrifice in Year 2 likely opens up about $2 million more in cap space for 2015, but the rest of his annual wages suffer by not taking the raise.

Meanwhile, Jackson emphatically said Anthony has to buy into this triangle-like new system that will promote sharing the ball and taking the load off him offensively. Otherwise, Jackson feels the Knicks won’t compete for a title anytime soon.

“It depends how quickly our team evolves,’’ Jackson said of how soon the club will be in title contention. “If we evolve as a team, we can do it rather quickly. If we’re still going to sit and rely on Carmelo to do everything, it’s not going to happen.

“We put that load on him, it’s not going to happen. That’s what we’ve wanted to assure him. We want to evolve as a team and that sometimes means the old buying into the system and giving in to the process. And the process can take time. Hopefully shorter time than longer.’’

The new regime believes Mike Woodson played Anthony too many minutes and didn’t set him up to succeed late in games as a result with a predictable offense. His final-minute shooting stats in close games were abysmal last season.