Consecutive home losses to Everton and Newcastle have left the Red Devils ninth in the Premier League, 12 points behind league leader Arsenal and seven off the top four.
"It's difficult, the fact we've lost five games, but we won't give up," Evans told MUTV. "We want to keep going to the end and the most important thing is when we put the Manchester United shirt on and go out at Old Trafford or away from home, we make sure we give everything as players."
David Moyes's side was unimpressive against the Magpies and the center back acknowledged a failure to re-enact the determined comebacks of the Sir Alex Ferguson era.
"If you look back at the game, we lacked a bit of sharpness in our passing," Evans said. "We were sloppy in possession, which allowed Newcastle to get control of the game. When we were going forward, the lack of sharpness in our passing stopped us from creating much up front.
"Usually, whenever we're chasing a goal at Old Trafford, especially at the Stretford End, we usually put teams under an enormous amount of pressure but we didn't produce that. It's disappointing, especially after losing in midweek. It's not often we lose two games on the run at home like that."
The Northern Irishman is now targeting Tuesday's Champions League clash with Shakhtar Donetsk as an opportunity to get back on track.
"It's a chance," he continued. "European football has maybe suited us this season. If you look at the Leverkusen game away [which United won 5-0], we produced a very good performance there. Our passing was very good and hopefully we can pick that up again in Europe."