The Reds got off to the perfect start at Anfield against Sion on Thursday when Adam Lallana gave them the lead within four minutes but Ebenezer Assifuah equalised in the 16th minute.
"We can bounce back immediately, we've got a great game to look forward to," Mignolet told the club's official website (www.liverpoolfc.com).
"Everyone knows it's a Merseyside derby on Sunday so we'll recover well after this game and make sure we're ready for kick-off time.
"If we can get a good result and the three points we'll be back where we want to be, so everybody will be focused."
Liverpool manager Brendan Rodgers, under pressure after his side's inconsistent start to the season, said it was important for his players to focus on football and not get carried away with the emotion of the derby.
"We go into the game against Everton and we will focus on our performance. The players will look forward to it," Rodgers told reporters.
"We are a point behind Everton -- I know the media and written press will build the game up but we will stay calm."
The derby has seen the most red cards of any Premier League encounter, according to league data, and Everton goalkeeper Tim Howard said the games meant so much to the city.
"They mean everything to the city, both Red and Blue, and it means everything to the players. It's electric, like nothing else," the U.S. international told the club's website (www.evertonfc.com).
"Derbies have always been blood and thunder and always exciting games and I don't think that's changed, certainly not in my time here."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Peter Rutherford)
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