Seven consecutive defeats in the league saw Hamburg drop into the bottom three and brought the end of Bert van Marwijk's reign at the club last month.
The Dutch coach was replaced by Mirko Slomka, who has eased their relegation worries with a win and draw in their last three matches.
However, Adler, who has made 20 league appearances this season, says a tough campaign has taken its toll on the squad.
"The current season is brutal (and) restless," he told the Hamburg Morgen Post. "However, our team can cope with pressure.
"We have so often fallen down, but after that then stood up again.
"We are also mentally stable. Many players did not know the explosiveness and implications of a possible decline.
"We now have to get a grip, we have adopted the relegation battle and are on a good path."
Several of Hamburg's key players, including captain Rafael van der Vaart, have been injured recently, and Adler believes the club have enough about them to pull clear of danger once everyone is fit.
"If our injured players come back, we simply have more footballing quality than other teams that are down there," he added.
