The Arsenal manager has come under increased pressure after a 3-1 home loss to Bayern Munich in the Champions League in midweek.
With the Gunners on the brink of Champions League elimination, a top-four Barclays Premier League finish is likely to offer their only hope of returning to the competition next season and they look set to go an eighth season without winning a trophy.
Arsenal have long been out of the title race and face an uphill battle to overhaul north London rivals Tottenham to get back into the top four.
The Gunners' healthy financial position means that it would not be a disaster in money terms for the club to miss out, but Wenger is refusing to consider that scenario.
"We want to be in the Champions League," the Frenchman said. "Financially we can live with [not qualifying], but on the sporting front, no. And the sporting front is the priority."
FA Cup and Capital One Cup exits against lower-league opponents have also marred Arsenal's season, but Wenger, whose side hosts Aston Villa, believes his players can regroup and have a strong end to the season.
"What we need is to be united and strong, and not to be destabilised by people who have strong opinions after one game," he said.
"I believe what is important is that the club always goes with the guidelines we have and does not change direction every time we lose a big game, that would lead to a disaster.
"A bad period for a club is also a good opportunity to show how united and strong you are. We have a good history of that at Arsenal."