The Toffees have begun their Europa League campaign in promising fashion and top Group H ahead of Lille's visit to Goodison Park on Thursday.
However, Martinez has been dealt a blow with Antolin Alcaraz picking up a serious shoulder injury, the Paraguayan joining the likes of Bryan Oviedo, John Stones, Kevin Mirallas and Arouna Kone on the sidelines.
But with Darron Gibson back in contention and Sylvain Distin set to replace Alcaraz, the Spaniard feels that he has the squad depth to cope with both European and domestic competition.
"What we want to do is grow into the competition and try to be as good as we can," he told reporters. "The first objective is to try get through [the group] and to do so would be a phenomenal achievement, looking at the teams in this group.
"There is no such thing as a weakened side; we made sure we had a big enough squad to feature in all the competitions. We have 23 outfield players who have all showed what they can do - now it's about having that competitive edge.
"We proved we are ready to face games having made changes and that doesn't mean we aren't taking things seriously.
"If we want to become a big club with a big mentality we need to be ready to face many games and I think we've responded really well."
The likes of Romelu Lukaku, Christian Atsu and Muhamed Besic were all brought in by Martinez during the close-season after Everton ensured a return to European football with a fifth-place finish in the Premier League last term and the manager is thrilled with how they have adapted to their busy schedule.
"In football, when you get injuries and suspensions, you have two options - you can start moaning about them and the other one is to use it as an opportunity or to look to the youngsters," he remarked.
"Once the window shut, we had a strong enough squad. We can cope with suspensions, injuries and the demands of the games. I've been very pleased with how we've adapted to the travelling and also playing Thursday and Sunday."