A run of just two wins from their last nine games in all competitions has seen the Gunners knocked out of the Champions League by Barcelona and exit the FA Cup following a 2-1 loss to Watford at the Emirates Stadium.
Arsenal's dismal form has severely dented their title hopes, as they trail leaders Leicester City by 11 points with a game in hand.
"We're aware that we don't just depend on ourselves, that's obvious... I think the only objective we need to set for ourselves is winning the eight matches we have left and then what will be, will be," Monreal told the club's website.
"It's not just down to us. Even if we do win all eight games, that doesn't mean we'll be champions but what does depend on us is winning those eight games."
After Watford ended Arsenal's bid to become the first club since Blackburn Rovers in the 1880s to win three FA Cups in a row, Monreal feels they have the perfect chance to exact "revenge" when they host the Hornets in the league on Saturday.
"We know it's going to be difficult against Watford because we only played them recently and they knocked us out of the FA Cup, but we're hungry for revenge. It's a completely different competition," the Spain international said.