English defender Garbutt, 21, made his full debut as Everton lost 3-2 at Newcastle United on Sunday.
Newcastle came from a goal down to condemn Everton to a third consecutive Premier League defeat.
Roberto Martinez's Everton are languishing in 12th spot with eight losses, in stark contrast to this time last season when they had only tasted defeat twice.
But emerging defender Garbutt is refusing to panic just yet.
"We've just got to keep going and hopefully a win will turn things around. It's hard," Garbutt said.
"If we're playing well we're then conceding sloppy goals, and if we're playing poorly we're still conceding goals.
"We're a tight-knit group and we need to stick together and battle our way out of it.
"We have to keep our heads up. There are going to be highs and lows and coming on the back of a season when we did magnificently it was about dealing with the expectations. It's been tough but I really believe we'll dig in and rescue this situation.
"It's too early to talk in terms of a crisis, although you will get talk like that in football. If you have a run of form like we have, you'll get criticised - simple as that.
"But to say it's a crisis is a bit premature. I believe in the squad we have - we've got the quality but we need a win to spark our confidence."
