The Austrian champions, who open their title defence next weekend, went ahead in the 14th minute when Marko Stankovic took advantage of a poor pass from Leon Osman and rounded debutant Everton goalkeeper Joel before finding the net.
Stankovic doubled his tally when he wrong-footed Joel from the penalty spot in the 37th minute after Shane Duffy was penalised for handball.
Everton quickly pulled a goal back through Greek striker Apostolos Vellios, who was left unmarked to head home a pinpoint cross from Leighton Baines.
Both managers made a host of changes at the interval, but Everton were unable to find an equaliser in the second half with Kevin Mirallas going closest when he was foiled by a timely intervention by substitute goalkeeper Ivan Kardum.
Despite the result, Martinez was happy with his week's work in Austria.
He told the club's official website: "The game was more of a physical exercise than anything else. It's been a very successful week.
"We've accumulated a lot of work and that's been exactly what we needed and it's given us a very good platform. Today was just to get a run out and we gave everyone 45 minutes more or less.
"We were playing against a side who are one week away from the start of their season and that's what we wanted - we wanted to push ourselves to the maximum from a physical point of view, and I thought we responded really well."