HOUSTON — Carmelo Anthony said he has no regrets about turning down the Rockets this summer, but acknowledged he took “a long, deep look at it’’ after Dwight Howard sold him hard.

Anthony made his first trip back to Houston on Monday since his ballyhooed recruiting visit July 2, when he met with the Rockets representatives in the morning and afternoon. Later that night, he met with Mavericks owner Mark Cuban in Dallas, where the Knicks play Wednesday.

The Rockets have recovered from Anthony’s rejection and are off to a 10-3 start.

“All that stuff was intriguing, all that stuff I took a real good look at,’’ Anthony said at the Knicks morning shootaround at Toyota Center. “The weather, the tax situation, things that come along with being here in Houston. I took a deep look at it.’’

The Rockets placed behind the runner-up Bulls in the Melo Sweepstakes, and some reports suggested even the moribund Lakers piqued his curiosity more than living in Texas. Entering free agency, Anthony said in a video interview with Vice Sports that moving his young son, Kiyan, to a different spot in the country would be a potential deterrent.

But one persistent center known as “Superman’’ kept the Rockets in the hunt. They were able to open cap space for a max deal by trading Omer Asik and having a tentative deal in place for Jeremy Lin.

“We had some great dialogue back and forth,’’ Anthony said of his discussions with Howard. “I talked to him. We talked about some things. Ultimately it came down to what I really felt and really wanted at that moment. We had some contact and conversations. He tried. He tried extremely hard. It didn’t have anything to do with Dwight or James [Harden]. It came down to my own personal decision.’’

Rockets legend Clyde Drexler, now a team broadcaster, was at the recruiting lunch with Anthony and team dignitaries.

“He went with his heart,’’ Drexler told The Post. “The heart’s a strong thing. He’s going to be a great player for a long time. He doesn’t get his due.’’

The Rockets are off to a great start despite not netting Anthony or second choice Chris Bosh and letting Chandler Parsons leave for Dallas. Instead of Anthony, they signed Trevor Ariza, a former Knicks draft pick. The Knicks have stumbled to a 4-10 record and look more like a lottery team than a playoff contender.

“Of course I know they’re playing very well,’’ Anthony said. “[But] it’s not something I say to myself: ‘I regret doing this, regret doing that.’ I can’t do that. It’s not my nature as a person. I would never sit down and ask myself: ‘What if?’ ’’

Controversy was attached to Anthony’s visit when a mockup of Anthony was shown on the arena’s billboards in a No. 7 jersey — which happened to be the number of then-Rockets point guard Jeremy Lin. The former Knick tweeted his disgust.

To Anthony, the whole week was a blur and has said he prefers not to go through a free-agent tour again.

“It was quick,’’ Anthony said of the Texas whirlwind. “I got a chance to meet some people, the owners. See some players I already knew. As far as memories go, there’s really no memories — just kind of the atmosphere that took place outside the arena, the whole week.

“It wasn’t just that week. Everything that led up to that week along with that week. It was a long offseason for me.’’

The Houston crowd likely will greet Anthony with derision.

“I can’t expect anything other than fans cheering for their own team,’’ Anthony said. “I don’t know if they feel disappointment. Even if I didn’t visit, I don’t think I’d be cheered anyway.’’

The Knicks get a break as Howard (knee strain) will sit a second straight game and point guard Patrick Beverley is also out with a hamstring injury.

Andrea Bargnani made the trip but coach Derek Fisher downplayed the chance of him suiting up in any of the three games after suffering a new injury — a calf strain.