The Toffees will go straight into the group stage of the tournament after finishing fifth in the Premier League table last season.
Everton could face an additional batch of at least six games in their campaign, which some managers have previously stated puts a strain on the squad.
"I think we are ready for it," Martinez told the club's official website. "I am aware of the demands and I think it's important that we are aware, but that's what we wanted.
"We do want to put ourselves under massive pressure in terms of performing week in week out in every competition that we are involved in.
"We need to build on [last season] and the best possible way is pushing ourselves even further, and to do that you need the European challenge."
Martinez guided the Merseyside outfit to Europe in his first season since moving to Goodison Park from Wigan Athletic.