O'Shea was forced out of the 3-2 success early in the second half to be replaced by Paul Scholes while Silvestre was the victim of a robust challenge from Francis Jeffers.
Silvestre incurred a knee injury in the tackle while Republic of Ireland international O'Shea suffered a thigh strain in the win at Old Trafford.
Red Devils manager Sir Alex Ferguson will assess the pair's condition on Saturday but the defensive duo are both unlikely to be fit for Sunday's trip to Middlesbrough.
"O'Shea is a hamstring while Mikael's is maybe a sore one with his knee injury and we will have to assess that tomorrow," said Ferguson.
"We will have to wait and see how the players are first (before deciding whether to sign a defender during the transfer window)."
As for the performance against The Toffees, Ferguson was satisfied with his players after making several changes to his starting line-up.
"I thought we played very well and our attacking play was very good," he added.
"It was good for the players who came in to have the chance to express themselves and stake a claim as Man Utd players."
Gary Neville's own goal had cancelled out Nicky Butt's opener for the hosts who earned victory through efforts from Kleberson and David Bellion.
The unfortunate Neville admits his intervention had a detrimental impact on United's pattern of play.
Neville said: "I thought my own goal affected the smoothness of the performance.
"We started brightly, our passing was good and then there was a bad mistake from me.
"They got a bit of a lifeline and put us on the back foot but our goal before half time changed the game around before we got a bit sloppy at the end."
