The Italian side slumped to a 2-0 defeat on Wednesday in Madrid as Atletico's Jose Gimenez and Diego Godin fired the Spanish side to a stunning victory.
The defeat puts Juve's backs against the wall heading into the second leg, where they will be forced to overturn a two-goal deficit at home without the benefit of a vital away goal.
Each of the last five times Juventus have lost the first leg of a knockout stage match in European competitions, they have been eliminated from the competition, but Chiellini believes this Bianconeri can avoid that fate heading into the second
"We knew they were very dangerous from set-pieces and we had to be more focused in those situations," Chiellini said post-match.
"We must remain calm because we can still do it. We have to reset our minds quickly and try to win in Turin."
Allegri echoed his defender's sentiments, saying he believes the team can overcome the deficit in the second leg.
To do so, they will need to avoid the mistakes of the second half, where they conceded two set-piece goals to Gimenez and Godin while nearly conceding another, only for VAR to rule out a finish from former Juve forward Alvaro Morata for a foul on Chiellini.
“The second half was ugly, as we made the mistake of following their lead. Atleti are very good at letting a game go by without a shot on goal," Allegri said.
“Now we have the chance to turn this around, we must have faith, we’ll have some players back and there’s no point crying over spilt milk. We knew it was going to be tough, that Atletico Madrid force you to play badly, with a slow tempo. We moved the ball quicker in the first half, but not in the second.
“We got the approach wrong in the second half. It’s that simple. These things can happen, there will be great disappointment after this 2-0, but we can turn it around. It won’t be easy, we need a great second leg, but it can be done and we must have faith.”
The two sides will collide in Turin for the second leg on March 12.