The Seagulls, who were already missing seven first-teamers for Saturday's 3-1 win, lost Buckley to a hamstring problem early in the second half.
Right-back Bruno also had to go off but assistant boss Nathan Jones revealed the Spaniard should be fine after suffering concussion.
"We are having to ride the punches with the injuries, nothing is easy and we have another injury with Buckley," said Jones.
"He has tweaked is hamstring, so we'll have to wait but Bruno will be okay. He has bit of concussion but it's not too bad."