The Reds fell five points behind the Gunners with their second defeat of the campaign and Mignolet is now looking for a positive response when they host Fulham at Anfield on Saturday.
"Everybody wanted to do well," Mignolet told the Liverpool Echo. "We were motivated and confident going into the game because it was a good opportunity for us to go top of the table.
"Unfortunately, we came across a good Arsenal side. They put us under pressure and scored an early goal. Afterwards, you're chasing the game a bit.
"At half-time we changed things and managed to create some chances, but we couldn't score a goal. Then Aaron Ramsey killed the game off, really.
"Arsenal are doing really well at the moment and they are a good side. That doesn't mean we're not disappointed, but the most important thing is that we can't drop our heads after this performance.
"We must look forward and make sure we put things right against Fulham. It's always important to respond after a defeat. I'm sure everybody will be prepared to work hard from Monday onwards for the preparation against Fulham."
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