Austrian Thiem completed a hat-trick of wins over the 20-time grand slam champion in 2019 with a 7-5 7-5 victory on the opening day in London.
Federer now faces a tough task to advance from Group Bjorn Borg, which also contains Novak Djokovic and Matteo Berrettini.
The 38-year-old committed 30 unenforced errors and won 11 of 22 points on his second serve in an uneven showing at the O2 Arena on Sunday.
"I thought he played well. The start definitely didn't help. That put me on the back foot a little bit," Federer said.
"But I recovered well and I thought the match was pretty even for a long period of time. I felt I had my chances. Didn't feel like I was outplayed or anything.
"Just maybe those first-round hiccups a little bit, not hitting your spots on the serve when you need to, getting into trouble early in the service games, which maybe doesn't happen later in the tournament."
Federer won the last of his six ATP Finals titles in 2011 and will have to be at his best to stay in contention for a seventh.
"It's a normal tournament from here on forward. I'm not allowed to lose anymore," the Swiss star said.
"That's how it is every week of the year for the past 20 years, so from that standpoint there is nothing new."
Both players are back in action on Tuesday as Federer faces tournament debutant Berrettini, who was no match for a dominant Djokovic.
The manner of the Serbian's 6-2 6-1 triumph and the tight schedule gives Thiem little time to savour his fifth career win over "probably the best player of all time".
"The system is pretty brutal, I would say, because I had an amazing victory," he said.
"I'm feeling great. I'm feeling now that I have a good chance to reach the semis, but if I lose on Tuesday, for example, everything is completely open again and I [would] have to worry about everything on the next match on Thursday.
"The only thing I can do is rest well [on Monday], practice well, and be fully focused again on Tuesday."