Thomas' round of 82 on Thursday, including a nine at the last hole, meant he was playing for pride in his second round and managed that with a level-par 71 in tough conditions.
The two-time PGA Championship winner has now missed the cut in four of his last six events and is struggling to make Zach Johnson's team for the match against Europe in Rome.
Thomas sits 13th in the U.S. Ryder Cup standings with only the top six guaranteed a spot and six more then selected by the captain. He knows he is running out of time.
"I want to make the Ryder Cup more than anything. I'm probably honestly trying too hard to do it," he told reporters at Royal Liverpool on Friday.
"It reminds me a lot of my first or second year on Tour. I tried so hard to make that team for the first time.
"I've been trying to make it easy on Zach and get in the top six, but I seem to not want to do that with my golf. I have a couple of events left to try to get in the playoffs and then make a little bit of a run and try to prove a point."
Despite his woes at Hoylake, Thomas said he actually played good golf but made too many "bonehead mistakes".
"Everybody has their waves, their kind of momentum and rides and rock bottoms, whatever you want to call it," he said.
"I just keep telling myself, this is it, I'm coming out of it, and I unfortunately have surprised myself a couple times with some bad rounds. It doesn't mean a day's good play like today doesn't get a spark going.
"There's nobody that shot 82 that hit some of the quality shots that I did yesterday. It doesn't make sense. I'll hit shots like a number one player in the world, and then I'll make a nine on my last hole of the tournament.
"I don't know if it's a focus thing or putting too much pressure on. When I figure it out, I'll be better for it."
Thomas has played in the last two Ryder Cups, compiling an enviable record, winning four points from his five matches in Paris in 2018 and 2.5 points in 2021.
Asked how he might convince Johnson to select him, Thomas said he hopes his record speaks for itself.
"It's not like I'm going to write him a love letter or anything. I would like to think that my record is my best argument," he said.
"I love the team events. I thrive in them. This is the first time since I first qualified that I'm relying on a captain's pick, and it's not fun, especially when you're trending the wrong way."