The Jets' starter since 2009, Sanchez tried to throw a practice pass on the sideline, but he shook his head after making one short toss - possibly a shake-off that gives Smith (16 of 32 for 199 and three interceptions) the starting job.
Sanchez had an X-ray of the shoulder and will have an MRI on Sunday. He left the stadium right after the game and was not available for comment, but his clothes remained hanging in his locker.
"We're going to compete all the way through," Ryan said when asked whether Smith was his No. 1 at this point.
"From Day 1 I said we will make the announcement on the starting quarterback when we think it's the appropriate time ..."
The quarterback situation has been the No. 1 question mark for Ryan's team since training camp opened. If Smith is the guy, he didn't look ready for prime time on Saturday.
"As long as Rex and the committee are evaluating us, I think I have a shot," said Smith, who stepped out of the end zone in the fourth quarter and gave the Giants a safety. "As I stated, I don't think one game, one practice or one day will tell you the type of quarterback I am."
"That's what he gives this team, the opportunity to hit some big plays," said Manning, who was 8 of 20 for 83 yards. "He's an explosive back with a lot of speed, and when he gets an opening he can make things happen."
After Sanchez was hurt, Simms took over.
Brown's other field goals covered 40, 33 and 50 yards.
"It's something we'll work on, see what's holding us back, what adjustment we need to make," Manning said.
The Giants' best drive came late in the half. Manning sandwiched passes of 20 yards to Jerrel Jernigan and 34 to Nicks around a 23-yard pass interference penalty against Kyle Wilson to get a first-and-goal at the Jets 4. Three plays netted 2 yards and Manning's fourth-down pass to Nicks was broken up by Dawan Landy.
NOTES: The severity of Brown's injury was not known after the game. Giants back CB Jayron Hosley sprained an ankle. ... Jets G Vlad Ducasse left the game early with an undisclosed injury. .. Wilson finished with five rushes for 92 yards. ... Jernigan had five catches for 66 yards. ... The Jets had five turnovers, four more than the Giants.
Copyright 2013 by The Associated Press