The Leos welcome Legia to Estadio Jose Alvalade for the second leg of their last-32 encounter after being held to a 2-2 draw in Poland last week.
Sporting's European exertions are proving a pleasant distraction from their struggles in the Liga, where they lie fourth with 13 points separating them and leaders Benfica.
Such performances saw Ricardo Sa Pinto named Sporting coach less than two weeks ago and defender Carrico believes Sunday's 1-0 defeat of Pacos de Ferreira - Sa Pinto's first win in charge - will help them against Legia on Thursday.
"All that matters is that it was a goal that got a win that gives us confidence," he told the club's official website, www.sporting.pt.
"We are working with a new coach now and we still have a lot of things to learn with him. With a bit of patience we will do that."
Sporting's fans have not been slow to voice their displeasure at times this season.
Carrico said: "It is completely normal in football [to be booed when you are not performing].
"This is a sport that is about winning and when that doesn't happen people boo.
"When we win a second or third game on the run, it will stop.
"This win will give the lads confidence for the Europa League game in the week."
Sporting boss Sa Pinto echoed the defender's sentiments, adding:
"The fans are saddened by the situation, wanted a stable team, with other results. It's understandable.
"The circumstances are such but we must have patience and to unite in support of the club.
"Only with great spirit of unity that can restore confidence to return to play the way that these players have played.
"It's a huge thrill for me and a great responsibility to train my team.
"I want to do better, return to Sporting self-esteem and confidence."
While buoyed by the Sunday's victory, Oguchi Onyewu and Fito Rinaudo both picked up injuries in the match.
United States international Onyewu is out of action for eight weeks with a knee problem, while Rinaduo picked up a sprained ankle that will keep him out for 10 days.
Meanwhile, Thursday's match will be the last time Maciej Rybus and Marcin Komorowski will appear for Legia.
The Polish side signed an agreement with the Russians during the winter transfer window and the duo will move on February 24.
