U.S. Open champ Djokovic's "huge sigh of relief" after match point

In an exhilarating match, Novak Djokovic became a two-time U.S. Open champion Sunday night after defeating Roger Federer 6-4, 5-7, 6-4, 6-4.

This was the 28-year-old's third Grand Slam title of the season and the 10th Grand Slam title of his career. The world's No. 1 player is now seventh on the all-time list of men's singles champions.

"All the way to the last point, I didn't know if I'm gonna close out the match in four sets. I was actually serving for the match at 5-2 in the fourth set. [Federer] came back, he kept pushing, he kept making me play the last shots and that's why he's been out there and he's been the most successful player in the history of the Grand Slams," Djokovic said Monday on "CBS This Morning." "And I was fortunate enough to come up with some big, big serves to get me out of trouble in the last game. When I saw his last return going out, it was a huge sigh of relief and that's all it feels."

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Novak Djokovic of Serbia celebrates in the fourth set against Roger Federer of Switzerland during their men's singles final match at the U.S. Open Championships tennis tournament in New York, September 13, 2015.
Shannon Stapleton/REUTERS

The rain delay was an added challenge to the match.

"It kind of builds the pressure and expectations, and we were both tense coming into the court," Djokovic said.

"You don't know what's coming up next. Are we gonna go out on the court -- we're warming up, we're cooling down. And the court was a little bit also moist and I had a nasty fall at the beginning of the match as well," he added. "So it was very tense, but this is what you expect when you're playing in the Grand Slam finals against one of the biggest rivals."

The crowd at Arthur Ashe Stadium seemed to pull overwhelmingly for Federer, who holds 18 Grand Slam titles but had not made it to the U.S. Open finals since 2009. At certain points, they cheered when Djokovic made unforced errors.

However, Djokovic pulled through and said he was impressed with the 34-year-old Federer's recent form.

"At his age, after everything that he's achieved in his career, he keeps on going, still fights so hard. I mean, I played back-to-back Grand Slam finals against him in Wimbledon a few months ago and now [in the] U.S. Open, and I feel like he's improving his game as he goes along."

Fans and critics have been buzzing about Federer's latest innovative shot, the "SABR" (pronounced "saber"), or "Sneak Attack by Roger," where he returns the opponent's second serve by charging to the net and chipping the ball back, sometimes catching the opponent off-guard.

"From an opponent's perspective, it's not really pleasant when he comes and uses SABR, but, yeah, I mean, this is why he's a great champion. He has this commitment and dedication to the sport, and it's quite remarkable to be part of his era," Djokovic said.

"Roger, Nadal, Andy Murray and myself -- we keep on pushing each other's limits," Djokovic said. "We keep on looking for room for improvement in our game."

Djokovic credits his mental toughness to his parents who helped provide opportunities for him to train in midst of rocky circumstances.

"Especially during '90s and wars and economic crisis of Serbia, it was very difficult for them to actually create such circumstances for me to become a tennis player, so I owe great gratitude to them," he said.

He also credited his first tennis coach, Jelena Gencic, who died in 2013.

"She had a very holistic approach to tennis and to life. It was not only about tennis, it was about the way you - how you lead your lifestyle, you know the way you approach life in general," Djokovic said.