The England skipper limped off midway through the second half after racing through the inside-right channel.
Rodgers gave no indication of how serious the problem was, but said the 33-year-old would be assessed in the next couple of days.
"It was his hamstring so we just need to see how it is," the Reds boss said in his post-match television interview.
"He was outstanding in his performance, the quality of his passing, but when he went to get that pass he felt a little tweak."
@popularpete Yes, England need some solid, injury free midfielders like Wilshere.- nickyb