United boss Jose Mourinho, who is trying to manage his squad before the Red Devils all-important Europa League final with Ajax on May 24, expressed his concern over the injury following the 0-0 draw at St. Mary's.
"Fellaini, on top of his experience, he says it's not a tear," Mourinho told MUTV.
"On top of his experience, he says it was a minimal thing but minimal can be a big thing. Let's wait for tomorrow but he needed to play.
"I couldn't protect him as he needed to play. He didn't play for three matches due to suspension. Players need not only to rest but also to play. He wasn't playing a lot so he had to play today. I don't blame myself or our decision but let's wait."
Mourinho also confirmed with Sky Sports that Eric Bailly was carrying a niggle.
"The one with little problems is the one [player] that can have little problems," he added. "Eric, because he's not playing the final [due to suspension].