The Blaugrana's influential No.10 will be out of action until early January due to a hamstring problem, while their first-choice goalkeeper will be unavailable for up to four weeks due to a calf problem.
However, Martino says Barcelona has adequate replacements for both men.
"We will be without the best player in the world and without the best shot-stopper in the world, but I have little doubt that we will cope without them. We have some great players to replace them," the Barca coach stated at a press conference.
"I don't think that we will be weaker because of our injury problems. Situations like this only make us stronger."
Martino then went on to dismiss suggestions that there will be more pressure on Brazil attacker Neymar now that Messi's sidelined until the New Year.
"Neymar has been doing very well ever since he got here and I don't think that his situation changes due to Messi's absence," he reasoned. "There's no extra pressure on him."
Neymar has so far netted four goals in 11 Liga appearances.