Gasquet booked his spot in the last four at Wimbledon for the first time since 2007 after stunning reigning French Open champion Stan Wawrinka on Wednesday in a gruelling five-set thriller, which ended 6-4, 4-6, 3-6, 6-4, 11-9.
"I'm proud because there are big players in the semis," Gasquet told reporters. "But I'm the worst when you see Federer, Djokovic and Murray and me."
The Frenchman knows that he will be in for another tough match against Djokovic in the semi-finals after the world number one cruised past Marin Cilic 6-4, 6-4, 6-4.
Gasquet has only beaten Djokovic once in their last 13 meetings, a victory whih came at the 2007 Tennis Masters Cup in Shanghai, where the 29-year-old triumphed 6-4, 6-2.
However, Gasquet is aiming to put up more of a fight than in their most recent encounter which saw Djokovic crush the Frenchman 6-1, 6-2, 6-3 in the round of 16 at this year's French Open.
"I want to enjoy it, to play a better match than I did in Paris," Gasquet said. "It's important for me to think I can win this match. That's the most important. To go on the court and think you can win, it's something I need to do it on my mental part, to be there to win.
"Novak is an incredible player to face in the semis of a Grand Slam. I want to enjoy that moment and to try to reach the final, of course.
"Novak is the favourite. Everybody knows that. But I want to take my chance and we will see what will happen."
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