There should have been a warmer moment at the net with Ajla Tomljanovic, after the three-hour, three-set battle, than just a cursory handshake. But Serena Williams has never lost politely at the U.S. Open. 

Otherwise, it was a perfect sendoff for Serena. 

Great run, great week, great match, great career. Three great nights at Flushing Meadows, where the 25,000 fans at 25-year-old Arthur Ashe Stadium never sounded louder. 

Williams was an aging, past-her-prime championship boxer who wouldn’t fall to the mat in the end. Down 5-1 and beyond exhaustion, she saved five match-ending, career-ending points against Tomljanovic’s serve. She punched herself out in the thrilling second-set tiebreak win. 

“I’ve been down before. I’ve been down like 5-1, I think, before and come back,’’ Williams said late Friday. “I don’t really give up. Yeah, I think in my career I never gave up.’’ 

She never gave up from the day she was born in Compton, Calif. That final game should be the last memory of Serena on a tennis court — even though it became a loss. 

Williams has hedged slightly since her announcement in “Vogue” last month that she was “evolving away from tennis.” On the “Today” show before the tournament, Williams responded, “Never say never,’’ and she repeated it on the court late Friday. 

Let’s hope it is never. Let’s hope this is 100 percent the end for Williams, who will turn 41 on Sept. 26 and is only going to get even slower. 

Let’s hope she goes out as gracefully as Pete Sampras did 20 years ago when he won the Open at age 31, then retired. We really haven’t heard from Sampras since. 

Let’s hope Serena doesn’t pull a Michael Jordan, the NBA GOAT who came back at age 38 and looked as ancient as the Washington Monument. 

We’ll certainly hear from Serena, who is addicted to attention. But hopefully it will be just about Serena Ventures, her investment firm. 

This won’t be like Tom Brady, but Williams cannot know how she might feel 10 months from now. 

If Serena had been crushed in the first round, this would not be an issue. But when Williams, one shy of the Grand Slam record of 24, says, “I think, honestly, what I’ll remember most is that my level was coming back,” there is room to fear an unretirement. 

“It makes it easier, but also it makes it a little bit harder,’’ Williams said of her rising play this week. “I was just getting better with each week.’’ 

This was wonderful sports theater — starting on opening night when the place shook as she walked onto the court. The Open will miss her dearly the rest of the fortnight. 

In her post-match, on-court interview, a teary Serena said: “It all started with my parents, and they deserve everything. These are happy tears. And I wouldn’t be Serena if it wasn’t for Venus.’’ 

Despite all the over-the-top, angelic plaudits she received the past few days and a heroine’s reception, Serena could’ve been a better on-court role model. My colleague Phil Mushnick has dealt with that. 

Even in the post-match celebration, you had to listen extremely closely to catch Williams mentioning her gallant foe from Australia. It is always about Serena, and across her career she rarely credited her foe after a defeat. 

But credit Williams for being self-deprecating about her past Flushing blowups late Friday. 

“I didn’t smash any racquets even, so that was a plus,’’ she said. “And I had a good attitude, even if I didn’t want to.’’ 

Serena, and Venus, brought reams of electricity and style to tennis during their voyage, so needed in this country because of the utter fail of the American men. 

Thank you for that, Serena, Venus and the great Richard Williams — who has been out of the public eye for years because of his ailing health. 

“I’m ready to, like, be a mom, explore a different version of Serena,’’ she said. 

Hope she really means it.