Jurgen Klopp hails Liverpool's 'statement' win over Everton
Mohamed Salah scored for the first time since Boxing Day and January signing Cody Gakpo bagged his first goal for the club as they snapped a four-game winless run and earned only their second win in eight games in all competitions.
"It was a massive relief," Klopp said. "The performance was a statement for us that we can do this ... It was the best game for a while.
"We have to carry on. To get out of our situation and to bring consistency, we need performances."
Liverpool, last year's runners-up, climbed to ninth with 32 points. They trail fourth-placed Newcastle United by nine before Saturday's trip to St James' Park.
Klopp said Liverpool had played like their true selves against Everton but that they had to keep delivering that level of performance.
"It felt like us, it looked like us," Klopp said.
"It was a really important night. It gave us all the signs that was us tonight, and now we have to make sure it is us from now on."