Carmelo Anthony tossed out a wonderful sentiment at Monday’s Media Day, explaining his decision to re-sign with the Knicks stemmed from not wanting to abandon them with “unfinished business’’ on tap.

Anthony admitted for basketball reasons, heading to the Bulls or Rockets may have been wiser, but wouldn’t have been appropriate after admitting to “forcing’’ his way to the Big Apple without delivering the goods. Anthony also didn’t shy away from predicting this season could be special, saying the Knicks “will be there at the end.’’

It was by far his most revealing explanation regarding his reasons for staying with the Knicks. Despite the team’s wishes, Anthony declined to hold a press conference after he re-signed for five years and $124 million.

He has spoken in dribs and drabs since, but never came close to Monday’s intriguing monologue, in which he said he “wouldn’t have felt right’’ leaving the Knicks after last season’s 37-45 catastrophe.

“It wasn’t all about running and jumping ship to get something in the immediate future,’’ Anthony said at the Knicks’ training facility in Greenburgh. “I’m willing to be patient. How long I’m willing to be patient, I can’t tell you that. I’m willing to take that chance. For me to get up and leave like that — now that I look back at it — I wouldn’t have felt right within myself.

“From a basketball standpoint, it probably would have been the greatest thing to do [to bolt for the Bulls or Rockets]. I wouldn’t have personally have felt right. I forced my way to New York and have some unfinished business to take care of. I wouldn’t have felt right getting up and leaving like that.”

Meanwhile, Anthony isn’t branding the Cavaliers’ new Big Three of LeBron James, Kevin Love and Kyrie Irving the heavy Eastern Conference favorites just yet. Anthony said he “applauds’’ his buddy James for returning to his hometown, but that was the end of the plaudits.

“What [LeBron] was able to do in Miami was special,’’ Anthony said. “As far as Cleveland goes, everybody has a clean plate right now. We’re all 0-0. Everybody starts today. We all have the same opportunity and have the same chance to put in the work and see what happens.’’

Anthony has a slimmer body, a new regime — led by team president Phil Jackson and coach Derek Fisher — and a new positive outlook after spending much of last season’s wreckage in a state of misery and confusion. He wouldn’t admit his free agency was a distraction last season, but did say his mind is clear and easy after re-signing.

“Anytime you have a new coach, a new energy comes along with that,’’ Anthony said. “You walk around the building and feel that energy. I felt that energy in the offseason. You see everybody is rejuvenated. At the end of the day, we’ll be there at the end. If we’re all in it together, I believe we will be there.’’

The Knicks gathered at West Point on Monday night and hold their first training camp practice Tuesday at Christl Arena. Over the summer, Anthony saw a different dedication from his mates than he did during the Mike Woodson Era.

“I saw this offseason the amount of time the teammates put in the gym working on what they needed to work on and got with the coaches,’’ Anthony said. “They were all together. Everybody is ready to take the next step and make that change — a new level of focus. You can just see the mind-set is a lot different. We still have to put that on the basketball court and have a great training camp.’’

Jackson sees a playoff club, and thinks the Knicks need 45 wins to get there. Anthony wouldn’t predict 45 wins but guaranteed they’ll be better than that.

“I agree with Phil and Fish,’’ Anthony said. “It’s me coming from a confidence standpoint, knowing that the pain I endured last year as a team, we don’t want to go back in that lane no more and feel that pain again.’’

Anthony’s decision to trim his body has given him a sharper mind-set and sleeker look.

“More for me, it’s mentally,’’ Anthony said. “My physical makeup, I feel awesome, feel great. I haven’t felt like this from a physical standpoint in a long time. It’s more the mental aspect where I’m going to be better at. I’m at a good place now — a lot of clarity and understanding.’’

He still hasn’t mastered the triangle but said he is on his way, saying it should “enhance” his game. He has spoken to Michael Jordan, Scottie Pippen and Kobe Bryant and is “distilling that information in a bottle.’’

“I got a good glimpse what the system will be,’’ said Anthony, who participated in voluntary scrimmages with teammates. “And it’s fun. I’ve been here three weeks early working with the guys, asking questions. Not just going out thinking I know it all [but] being receptive. I know it’s not going to happen overnight. My main thing is embrace it, the new regime and new system, and along the way have fun.’’