The fullback had been out for five months, but lasted an hour at Goodison Park and hopes to face Standard Liege this week.
Hibbert told evertonTV: "I felt very, very tired afterwards (on Saturday). It was hard trying to come back and maybe I could have done with a couple of games before this one.
"I have been back training for a week and I felt alright in the first half.
"I was thankful that the gaffer gave me the nod and any local lad wants to play in the derby."
Everton take a 2-2 draw into the second leg of the clash with the Belgian champions, with victory in Liege or a high-scoring draw required for progression.
"It is a very big game," declared Hibbert, whose family were regulars on the supporters' European trips last season.
"The family keep me informed of the way days and it's great for the fans to have these trips.
"It is another cup and I think we should be better than what we are at the moment."