"Whether or not it will require surgery remains to be seen," said Steelers coach Mike Tomlin.
Taylor was not confident about returning for the opener. When asked whether he'd be able to return for the Sept. 11 game against the Baltimore Ravens, Taylor said he didn't know.
The Steelers were dominated by the Redskins, who outgained the visitors 259-129 in the first half and 452-186 in the game.
The Steelers' starters played one series while the Redskins' starters played the entire first half.
The Steelers did tie the game before the half on a 22-yard run by Isaac Redman, who broke a tackle at the line of scrimmage and scored with the help of a downfield block by wide receiver Antonio Brown.
Brown also caught 4 passes for 64 yards and was the only Steelers player to draw unsolicited praise from Tomlin.
"Antonio Brown appears to be in great physical condition, but we knew that before we stepped in the stadium tonight," Tomlin said.
Redskins kicker Shayne Graham missed two first-half field-goal attempts, but incumbent kicker Graham Gano kicked field goals of 29, 34 and 45 yards in the second half to provide the margin of victory.
Redman led the Steelers with 42 yards rushing on 5 carries. Grossman was the star of the game for the Redskins. The quarterback completed 19 of 26 passes for 207 yards and a touchdown.
Tomlin took the loss seriously.
"That's not the kind of performance we were looking for, hoping for tonight," he said. "Quite frankly we got outplayed in just about all areas: blocking, tackling, running, throwing, kicking.
"That team was better prepared tonight than us. They showed it. We accept that, and I look forward to this group responding to what we put out there tonight and understand that we've got a lot of ground to cover. But such is life. I'll expect these guys will respond accordingly. We'll go back to work, assess this performance. It needs to get better quickly."
"Those guys of course coming of offseason injury hadn't practiced enough, particularly to my liking, to sit them out there," Tomlin said. "We're going to continue to work with those guys and hopefully they'll be ready to go next week."