Goals from Sadio Mane and Mohamed Salah gave Jurgen Klopp’s side all three points against the Blues at Anfield.
“We have to qualify – that’s it, that simple,” Hazard told Chelsea’s official website.
“We want to play in the Champions League next season so the only solution is to be in the top four or win the Europa League.
“It’s not just about me, the club has to be in the Champions League. We miss the Champions League this season, so for the fans, for the board, for the players, the staff, this club has to be in the Champions League every year.
“But in the Premier League you never know how many teams can be in the top-four race, six or seven, so it is a hard challenge, but we can do it.
“Every year is different, every year is hard, but I think the Premier League is getting harder every year. But in the end, the target is always the same, to win something and then play