The champions beat the Reds 3-1 on Monday, just four days after Claudio Ranieri was sacked, to lift themselves out of the Premier League relegation zone.
They are two points above the bottom three and host fellow strugglers Hull on Saturday with caretaker manager Craig Shakespeare aiming to cement his chances of the job.
Shakespeare has backing from within the club and the squad and Fuchs knows the importance of continuing their revival following Ranieri's controversial exit.
He told the club's official site: "There were lot of things written in the media but it fired us up and we wanted to show what we were made of with a lot of untruths written. You saw the Leicester from last season.
"Every game for us is now a final, we want to stay in the league and we can build on that game.
"We were fired up from minute one. This season we were trailing a lot but were were going up 1-0, 2-0 and even 3-0. It's good for our game, it didn't happen too often until now.
Philippe Coutinho pulled a goal back for Liverpool but they missed the chance to return to the top four, leaving boss Jurgen Klopp to say they are all fighting for their futures.
Liverpool have dropped out of the title race, been dumped out of the FA Cup by Wolves and lost in the EFL Cup semi final to Southampton since the turn of the year.
Monday's loss left them with just two wins in their last 12 games ahead of Saturday's visit of fourth-placed Arsenal.
"After every defeat it's important to bounce back," Georginio Wijnaldum told the club's official site, with Liverpool fifth. "That's what we have to do on Saturday.
"Of course, it's difficult, and it's a hard one, especially with the way we lost the game. It's really sad. The manager (had) told us already at the beginning of the week, and again when (Claudio) Ranieri (left), that it was going to be a really difficult game.
"They want to show that they are a good team and they wanted to fight to beat us. We were not ready at the beginning of the game. We didn't adapt well in the game."
