Roberto Martinez's side put their stuttering Premier League campaign behind them to register an impressive 4-1 triumph at the Stade de Suisse last week, thanks in no small part to Romelu Lukaku's hat-trick.
The result perhaps flattered Everton, as Young Boys took the lead and enjoyed plenty of chances, while confidence in the Swiss side will have been rejuvenated after they secured a 4-2 win over Basel on Sunday to breathe new life into the Super League title race.
Everton head to in-form Arsenal three days after the second leg at Goodison Park, but Republic of Ireland international McCarthy wants no let-up from his colleagues when Young Boys visit.
"Arsenal's another big game in the league, but we first have to take care of Thursday," said McCarthy, whose oft-hamstrung season has mirrored the frustrations of his club.
"We have a big lead but we won't take any prisoners. We have to put a show on and it is two big games coming up.
"It has been a frustrating campaign in the league especially. I think we have been sticky at times.
"But, we have come back from a great result in Europe and we need to try and get the wins at home. The fans have come out in their numbers and we need to go again on Thursday.
"The fans need to stick with us. I am sure we will bounce back on Thursday."
Victory over Basel was just Young Boys' second since resuming action after a long mid-season break earlier this month.
Making his first start since suffering a serious ankle injury against the same opposition 12 months previously, Alexander Gerndt's early double set the Bern club on their way.
The Swede may again play from the start after being withdrawn early at the weekend and he is looking forward to making another good impact.
"A fairy tale, that's a good description," Gerndt said when asked to sum up his comeback.
"It's a great feeling. I'm on the way back, but I have not yet reached my full potential."
Young Boys' goalscorer from the first leg, Guillaume Hoarau, also netted against Basel, leaving coach Ulrich Forte beaming.
"He was as cool as ice," Forte said. "He did not just score two goals, but he put in a lot of work with Sekou Sanogo and Hoarau off the ball.
"Therefore our ability to press was so much better."
With Young Boys' attack now bolstered, Everton may have to deploy a makeshift defence with John Stones suspended after his red card in Bern, while Leighton Baines and Bryan Oviedo are both returning to full fitness at left-back.
