LONDON, July 1 (Reuters) - Ukraine"s Elina Svitolina admitted she was struggling mentally with the demands of trying to win her first Grand Slam title as she joined the exodus of top seeds at Wimbledon on Thursday. The world number five, seeded three, was beaten 6-3 6-4 in the second round by Poland"s Magda Linette, meaning that six of the top 10 seeds have already departed in the women"s draw. Sofia Kenin (4) and Bianca Andreescu (5) were knocked out on Wednesday, while sixth seed Serena Williams, a seven-time Wimbledon champion, had to retire from her first round match after slipping and injuring her leg on Tuesday. read more Ninth seed Belinda Bencic and 10th seed Petra Kvitova, a two-time Wimbledon champion, lost in round one. Svitolina is regularly amongst the top seeds at Slams but the Ukrainian has yet to make the breakthrough many predicted. In 34 Grand Slam appearances, the 26-year-old has managed to reach two semi-finals, at Wimbledon in 2019 and the U.S. Open a few weeks later, but has only reached one quarter-final in her last five attempts. Against Linette, who had never beaten a top-10 player before and had lost in the first round at Wimbledon four times, Svitolina lacked inspiration and admitted she was struggling mentally and that her game was not in the best shape. "Today I was not really in a good place. I need some time to analyse, but I think mentally it was not very good for me today," Svitolina told reporters. "When you play a Grand Slam it"s a different kind of pressure. It"s tough to handle, but is part of the job. "Today probably I was not fresh mentally to do that. I have been on the Tour for years now and there have been different kinds of situations. But right now I wouldn"t say it"s a very smooth time in my career..." Svitolina"s hopes of winning a major are not helped by the incredible depth in the women"s game -- illustrated by the fact that four of the semi-finalists at this month"s French Open were at that stage of a Grand Slam for the first time. Unseeded Czech Barbora Krejcikova, better known for doubles, went on to win the title at Roland Garros. read more "I think there has been a lot of talk about that for the past two years. There has been a really big race in the women"s game where anyone can win any tournament. "Everyone seems like the same level. So I think that"s what"s really changed. It"s like physically everyone is ready to beat you."