Regrets, Glen Sather has but one as it applies to his 19-year tenure at the top of the Rangers’ organizational management chart that, The Post has learned, will come to a conclusion as soon as a successor is hired as team president.

“I certainly would have been happier about it if we’d won the Stanley Cup,” Sather told The Post Thursday afternoon at the practice facility after informing the team of his decision to step back into a senior advisory role. “We had the opportunity to do it, but those three overtime losses in the final in LA…that’s the biggest regret.

“But then also the reality that we were starting to get older — not me personally, but the team — and we could see that we would need to make changes to get better. That’s always painful.”

Sather, who will work closely with Garden chairman Jim Dolan on the search for the Rangers’ president that will begin immediately, said that he hoped to have a successor in place “by July 1, but if we could do it by the [June 21-22] draft, that would be great.

“I can recommend the guy, but it’s Jim’s choice in the end.”

Sather also told The Post that Jeff Gorton’s job is safe as general manager.

“I wouldn’t be doing this if our management was in chaos,” said the 75-year-old Sather, who has had a steady full-time job in hockey since turning pro in 1964-65 with the CPHL Memphis Wings. “I think Jeff has done a hell of a job. Look at some of the deals he’s made. Jeff is not the kind of guy who misses very much. He built that team in Boston that went on to win the Cup.

“Our coaching staff communicates well and teaches, David [Quinn] has done an outstanding job bringing these young kids along. Chris [Drury, assistant GM] has been outstanding. We’ve got a group that works hard, communicates well. It was a very difficult decision for me, but I made it knowing that we’re in good hands.”

That said, the new sheriff in town will ultimately be the judge of that. When, for instance, Brendan Shanahan became president of the Maple Leafs in April of 2014, he retained general manager Dave Nonis and coach Randy Carlyle for one season before replacing them with Lou Lamoriello and Mike Babcock, respectively.

Things will change, perhaps even dramatically, if not immediately.

Sather said he will maintain his residence in New York. “I’ll be around,” he said.

He will continue to lead the hockey department while the search is ongoing and will preside over the organizational meetings, set to commence on May 5, and all functions leading up to the draft.

“I told my wife, Ann, about the meetings, and she reminded me that’s the day of our 50th wedding anniversary,” Sather said. “She said I must have scheduled the meeting so I wouldn’t have to take her out. The truth is, like so many guys, I forgot. How many times in my career did I have May 5 free? Not many.”

Sather is the Last Lion of Winter, the remaining survivor of a time when general managers with big personalities commanded the room and owned the league. Sather in Edmonton, Bill Torrey on the Island, Emile Francis in St. Louis and Hartford, Harry Sinden in Boston, Cliff Fletcher in Calgary and Toronto, Punch Imlach in Buffalo. They were colossus.

“Different times,” said Sather, who back in the day wore a smirk not even Bobby Bonilla could have wiped off his face. “The business has completely changed, the salaries these players make today, the revenue has changed, media and television have changed. It’s a big business.

“But in one way, it’s the same. Because it’s a people business. In order to manage people, you have to respect people. I think if you make a promise you have to fulfill it. You have to tell the truth. But respect is the main thing.”

Sather has mellowed. There is no doubt about that. But the game has mellowed. Fewer big personalities. The game has lost something. It is losing something special in Sather, hardly perfect and ultimately unable to live up to the bravado he brought to New York from Edmonton in June of 2000.

The early days were in fact chaotic, four consecutive playoff misses on top of the three misses that marked the end of Neil Smith’s run as GM. But Sather and the Blueshirts thrived after the introduction of the hard cap in 2005-06.

The Rangers, under Dolan’s ownership and Sather’s stewardship, became one of the most stable operations around, with two general managers and four coaches (Tom Renney, John Tortorella, Alain Vigneault, David Quinn) over the last 14 seasons. The Blueshirts went to the playoffs 11 times in a 12-year stretch beginning on 2006, and won eight playoff rounds from 2012 through 2015 while advancing to the final in 2014 and taking the Presidents’ Trophy the following season.

All the while, Sather was dealing first-rounders to get the one difference maker, the one player who could put the Rangers over the top. One for Rick Nash. Two for Marty St. Louis. One for Keith Yandle.

“I don’t think it does any good to second-guess,” Sather said. “We had a plan, a really strong team and I thought we had a great opportunity to win by making those deals. I’m sorry it didn’t happen. We sure tried.”

Sather probably won’t need a monthly MTA card once he hands over the presidency. He and his beloved bride will travel. He will live life outside of hockey, devote time to his family, spend time at his spread in Banff and the western White House in southern California.

“There’s not a hell of a lot of time left to do things,” he said.

But there was time for Sather to impart some of his wisdom to the Rangers he addressed on Thursday.

“I told those guys that they have an opportunity to play in the NHL, a lot of them for the first time, and not to piss it away,” he said. “I told them, ‘This is your time, don’t give it away.’”

The last half-century has been Sather’s time. Now The Last Lion of Winter exits. And a new time begins for the Rangers.