Bilbao are poised to secure fourth spot in La Liga and clinch UEFA Champions League football for the 2014-15 season, after Sociedad competed in the continental group stages earlier this season.
Real Sociedad are still Europe-bound, with a spot in some form of the UEFA Europa League next season guaranteed; whether it is starting in the group stages, play-off or third qualifying round is yet to be decided.
But Martinez said winning the Basque derby at San Mames on May 11, would be some consolation for Sociedad fans.
"That could be what hurts our fans most of all, that we're not going to the Champions League and Bilbao are in fourth," Martinez said.
"Such things happen though and they've had a very good season.
"We've still got the derby to play though, which will be our most difficult game, but it will be more for the pride of beating them, than for the points and that's a game we really want to win."
Furthermore, Martinez dismissed speculation he might switch to Bilbao in the off-season, claiming he would never move to Sociedad's arch-rivals.
"There's nothing in it," he said of the speculation.
"I don't think Athletic are going to come here offering €30million to their enemies at all.
"On top of that, I'd never head over to the other side, so the fans can be calm that'll never happen."
Martinez rued their failure to finish in the top four in Spain to back up their breakthrough campaign in 2012-13 but conceded he wanted the fans to have high expectations of the club.
"Not everyone can say the same but I know that there are some fans who aren't satisfied just with us getting into Europe," he said.
"It's been a season with a lot of games and in the end, we've achieved one of the objectives we set out with. Now there's three games left for us to push for fifth place.
"There always should be these demands.
"If there's no pressure from the outside, you can relax. That pressure is good, we should always want to achieve and do better.
"This season is something to be happy about, although our play hasn't been as good as last season.
"What matters most is improving and always getting three points."
He added: "The numbers are there, one of the main aims at the start was to get back into Europe again, though getting back into the Champions League twice in a row is very difficult for a team like Real Sociedad. We know we have the potential and could have reached fourth place. We always have to reach as high as we can, but we weren't able to do it this season. What matters though, is that we keep working hard right to the end."
