The Brazilian midfielder was sent off during the second half after catching Luis Suarez in the chest with a high boot.
Andre Villas-Boas' men were two goals down at the time and went on to ship three more goals in a painful defeat.
When asked if the club would appeal Paulinho's dismissal, Villas-Boas said: "I will try. Hopefully there can be some sensitivity into it, but we will look into it."
Elaborating on his frustration, Tottenham's head coach added: "I think the sending off is a bit harsh. I agree that Paulinho raises his foot high, but he doesn't have [the] intention to hurt Suarez.
"I think a yellow card is more appropriate.
"That was the key moment in the game; it didn't give us chance to bounce back and we suffered a heavy defeat."