Djokovic himself insists he isn’t keeping tabs on his unbeaten run, which reached 38-0 this season — and 40 consecutive victories dating to December — thanks to a 6-2, 6-1, 6-3 win over Thiemo de Bakker of the Netherlands in the first round of the French Open yesterday.

“I’m not counting,’’ the second-seeded Djokovic said with a smile. “I’m not trying to think about the streak that I have, even though it’s definitely something that makes me proud.’’

Others certainly are thinking about it. Indeed, it’s the talk of the year’s second Grand Slam tournament. Straight-set victories yesterday at Roland Garros by other top players such as Roger Federer, top-seeded Caroline Wozniacki, or defending champion Francesca Schiavone — and even 2010 semifinalist Tomas Berdych’s surprising five-set loss to a French qualifier — didn’t merit as much attention as Djokovic did.

The Serb, who won his second Australian Open title in January, is closing in on the Open-era record for best start to a tennis season by a man, John McEnroe’s 42-0 in 1984. He’s also only the sixth man in the Open era to win 40 matches in a row; Guillermo Vilas set the high of 46 in 1977.

But Djokovic’s pals on tour aren’t exactly making a big deal about it at the moment.

“In the beginning — I know him very well — I’d kind of joke, ‘Hey, let someone else win.’ Now you almost stay away. It’s almost like a pitcher going for a no-hitter,’’ said the highest-seeded American, No. 10 Mardy Fish, who beat Ricardo Mello of Brazil, 6-2, 6-7 (9-11), 6-2, 6-4.

Back on April 1, Djokovic moved to 23-0 this season by beating Fish in the semifinals in Key Biscayne, Fla.

Djokovic then defeated No. 1-ranked Rafael Nadal in the final there, part of a 7-0 mark against him and Federer in 2011. Victories over Nadal — who begins his bid for a record-tying sixth title at Roland Garros today — on clay at Madrid and Rome this month have many believing Djokovic could become the first man to win the Australian and French opens in the same year since Jim Courier in 1992.

Djokovic called it an “amazing streak,’’ and acknowledged that he never could have expected to be unbeaten in late May.

“I’m really trying to have the right mental approach to every match that I play, try to think about only winning, about [my] next opponent,’’ Djokovic said.

In the second round, he’ll meet 60th-ranked Victor Hanescu of Romania. Win that, and Djokovic could take on 25th-seeded Juan Martin del Potro of Argentina. The 2009 US Open champion hasn’t been the same player since right wrist surgery last year but got past 6-foot-10-inch Ivo Karlovic of Croatia, 6-7 (5-7), 6-3, 7-5, 6-4.

Berdych, the sixth seed, made a quick exit, blowing a two-set-to-none lead in a 3-6, 3-6, 6-2, 6-2, 9-7 loss to 140th-ranked Stephane Robert.

Two other seeded men lost: No. 22 Michael Llodra of France, and No. 26 Milos Raonic of Canada. Llodra left on an ugly note, likening the atmosphere at his court to an Arab marketplace after receiving a warning from Moroccan chair umpire Mohamed El Jennati for throwing a ball at a female security guard in the stands.