"She's very much a star, It's very clear, she's very important to the game" - Naomi Osaka on Coco Gauff after San Jose 2R loss

Naomi Osaka was outclassed by Coco Gauff, 6-4, 6-4, in a blockbuster second-round clash at the Mubadala Silicon Valley Classic on Thursday.

Post-match, Osaka had only kind words for her 18-year-old foe, who earlier likened their budding rivalry to that of Roger Federer and Rafael Nadal – fierce on the court but friends off it.

Indeed, Osaka displayed the respect seen between great rivals Federer and Nadal as she described Gauff as a "star" in a post by WTA Insider on Twitter.

Osaka on Gauff: "She's very much a star. It's very clear. She's very important to the game.

"After RG last year when I withdrew, she was the 1st player to message me and I've never forgotten that. I have so much love for her and I think she behaves well beyond her age." https://t.co/Z3sSMwobzi

"She's very much a star. It's very clear. She's very important to the game," said the four-time Grand Slam champion Naomi Osaka.

Gauff, who is likely to achieve Osaka's success and maybe more, leveled her head-to-head with the Japanese at 2-2.

Osaka also revealed that Gauff was the first player to send her a message when she withdrew from Roland Garros last year. It was then that the Japanese star opened up for the first time about her mental health concerns, citing her struggles with depression and anxiety.

"After RG (Roland Garros) last year when I withdrew, she (Coco Gauff) was the first player to message me and I've never forgotten that. I have so much love for her and I think she behaves well beyond her age," said Naomi Osaka.

Prior to her match against Osaka, Gauff sang the praises of her opponent, noting how she was "such a champion on and off the court" and is the type of person one would want to play against.

A statement performance under the sunset 🌅

🇺🇸 @CocoGauff defeats former World No.1 Naomi Osaka, 6-4, 6-4 in San Jose!

#MubadalaSVC https://t.co/2s1RUARwzh

Gauff faltered with eight double faults but managed seven aces to aid in her 88-minute victory. She won 85% of her first serve points.

The recent French Open runner-up was broken once as Osaka converted her lone opportunity late in the second set, but Gauff converted three of her 12 break points against her older foe. The American produced 19 winners to Osaka's 12.

"I realized I've been letting people call me mentally weak for so long that I forgot who I was; I lost today but I feel really confident in who I am" - Naomi Osaka

Naomi Osaka remains positive despite her loss to Coco Gauff

Naomi Osaka has been open about her mental health struggles since quitting the French Open last year. After her second-round defeat against Coco Gauff in San Jose, Osaka said that the outcome of the match had not affected her belief in herself.

She said that allowing people to call her "mentally weak for so long" made her forget who she was. It wasn't that way today.

"When I was playing, I realized I've been letting people call me mentally weak for so long that I forgot who I was. I lost today but I feel really confident in who I am," said Naomi Osaka in a tweet by the WTA Insider.

She also said that she was happy that she didn't let the pressure get to her during the match.

"I feel like the pressure doesn't beat me. I am the pressure. I'm really happy with that," said Osaka.

From 5-1...to 5-4!!! 😰

@naomiosaka saves 7 match points and looks to level up in the second set.

#MubadalaSVC https://t.co/zk33JYbYnZ

Osaka channeled her inner champion as she launched a late fightback in the match, saving four match points to hold at 5-2 in the second set. She then broke Gauff and erased three more match points to hold serve in the ninth game.

There was no other opportunity for Osaka as Gauff eventually sealed the match on her eighth try.