After withdrawing from last week's Madrid Open with lower back pain, Federer was just glad he was able to play two matches on the clay in Rome.
''It doesn't matter how I played. (What is) important is that I didn't have any setbacks and I was able to step on the tennis court and that I tried what I could with what I had,'' said Federer, who defeated German teenager Alexander Zverev in straight sets on Wednesday.
''I knew I wasn't good enough for any result here, so that's why I hope you don't read into it so much, and I don't,'' Federer said. ''This is like, `Who cares about the results here?' It matters what comes now in the next couple of months.''
With only 10 days before the French Open, however, Federer needs to figure out how to manage the pain.
''Time starts ticking more towards Paris,'' said Federer, who also missed 10 weeks this year after surgery on his left knee to repair a torn meniscus. ''The way I'm playing right now is never going to be enough for any good run in Paris, and then I also wouldn't play this way. I'm still confident I will be fine somehow.''
Meanwhile, top-ranked Novak Djokovic and seven-time Rome champion Rafael Nadal set up an attractive quarterfinal at the Foro Italico.
Djokovic overcame a horrendous opening set in a 0-6, 6-3, 6-2 win over 37th-ranked Thomaz Bellucci, and Nadal ground past Nick Kyrgios 6-7 (3), 6-2, 6-4.
It was the first time Djokovic was bageled in a set since a loss to Federer in the 2012 Cincinnati final.
On a cool evening, Djokovic struggled to find his range early on, committing 16 unforced errors to Bellucci's three in the first set alone.
When Djokovic finally held serve in the opening game of the second set, he raised his arms in mock triumph, drawing applause and amusement from the crowd.
Also, Andy Murray rolled past Jeremy Chardy 6-0, 6-4, and will next face 12th-seeded David Goffin, who routed eighth-seeded Tomas Berdych 6-0, 6-0 in 49 minutes.
Thiem's quarterfinal opponent will be sixth-seeded Kei Nishikori, who beat Richard Gasquet 6-1, 6-4.
Juan Monaco of Argentina upset French Open champion Stan Wawrinka 6-7 (5), 6-3, 6-4 and will meet lucky loser Lucas Pouille, who beat ninth-seeded David Ferrer 6-4, 6-1.
In the women's tournament, top-ranked Serena Williams came back from 5-3 down in the opening set and saved a set point in the tiebreak to beat American qualifier Christina McHale 7-6 (7), 6-1.
Williams was sick on Wednesday after trying some of her dog's food, but said she felt fine on Thursday.
''Unfortunately, it was true,'' said Williams, who first shared the news on Snapchat. ''I'm not the most serious person off the court. On the court I am, but off the court I don't have a serious bone in my body.''
Williams' quarterfinal opponent will be Svetlana Kuznetsova, who beat Daria Gavrilova 6-2, 2-6, 6-3.
Also, Timea Bacsinszky beat eighth-seeded Carla Suarez-Navarro 5-7, 7-5, 6-2; Irina-Camelia Begu defeated Daria Kasatkins 6-1, 6-4; Misaki Doi of Japan eliminated Johanna Konta of Britain 4-6, 7-5, 6-2; and Madison Keys made the last eight overcoming Timea Babos 7-6 (2), 6-3.
Federer went up a break early in the first set but Thiem broke right back, and Federer made little impact on the Austrian's serve the rest of the way. At 22, Thiem is the youngest player in the top 20, and second to Djokovic in wins on tour this year.
Federer decided not to run back to the middle of the court after a couple of weak backhand returns - heading straight for his chair instead as Thiem hit easy winners into the open court. Rome remains one of the few important tournaments that Federer has never won. He's a four-time runner-up at the Foro, including last year.
Andrew Dampf on Twitter: www.twitter.com/asdampf