South African Pienaar lasted only 10 minutes of Saturday's 2-2 draw with Arsenal before picking up a groin problem, while Belgian striker Lukaku, who moved to Goodison Park from Chelsea on a permanent basis this season, hurt a toe.
"They have both been assessed," Martinez told a news conference on Tuesday.
"Stevie P is going to miss the game at the weekend. He is the one that is going to take a little bit of time.
"Stevie is going to be out and he is going to join Arouna Kone and Bryan Oviedo, who are the only other two players that are not available.
"Romelu, we will keep assessing him. He has reacted well in the 48 hours after the game.
"At the moment it is too early to know if he will be available at the weekend but I am quite positive with Rom."
Gibson missed much of last season after hurting his knee while playing for Ireland but was back to full fitness despite not appearing against Arsenal or the opening day draw with Leicester City.
"Darron Gibson is fully fit and I consider him part of the squad," Martinez said of the former Manchester United midfielder. "He will be ready from now on to join the group and compete for a place."