NEW YORK, Sept 7 (Reuters) - As world number one Novak Djokovic slammed the door shut on American wildcard Jenson Brooksby on Monday, it also left the host nation without a player in the quarter-finals for the first time since the inaugural tournament 140 years ago. American players have won 85 men"s and 92 women"s singles titles at the tournament, which was first held in 1881 as the U.S. National Championship. Three U.S. men, including 22nd seed Reilly Opelka, and one woman reached the fourth round of this year"s hardcourt major but all four were defeated. "We have I think 14 or 15 Americans in the top 100, so we"ve got a huge group of guys there. We just don"t have the world beaters," Opelka, who lost to unseeded South African Lloyd Harris on Monday, told reporters. "I don"t think we will have a (Pete) Sampras, (Andre) Agassi era of just dominance like that again. It"s rare for any country. "It"s frustrating. You look at the States and you"ve got over a dozen guys in the top 100, and you don"t even really have a Grand Slam finalist. I feel like it"s just a matter of time before one of those ... can break through." The United States has not had a men"s major champion in 18 years with Andy Roddick the last to win a Grand Slam when he triumphed at the U.S. Open in 2003. There is a host of American women in the top 100 with 2020 Australian Open champion Sofia Kenin, the highest ranked at sixth, the last to win a major. Serena Williams, who won six of her 23 Grand Slam titles at the U.S. Open, has made it to at least the quarter-final stage in each of her last 12 visits to Flushing Meadows but both the American great and Kenin missed this year"s event. Shelby Rogers stunned Flushing Meadows by beating world number one Ash Barty in the third round but was then denied a quarter-final spot by British 18-year-old Emma Raducanu. Opelka predicted 20-year-old Brooksby, who is ranked 99 but is expected to jump into the top 40, would soon be in the mix at the majors, and Djokovic said he was also a fan, predicting after his match that "America has a bright future in tennis". Brooksby, playing for the first time on Arthur Ashe Stadium against a player chasing a calendar-year Grand Slam, showed he had the weapons to succeed on the biggest stage. "It"s definitely all positive things to take away," he said. "I learned my game. I"m feeling really confident in my game. I believe I can compete with anybody."