The Uruguay striker looked set to leave Anfield before the start of this season as he made no secret of his desire to play in Europe's premier club competition.
Liverpool held on to their prized asset and his value has soared further due to his outstanding form since his return from a 10-game suspension for biting Chelsea defender Branislav Ivanovic last season.
Suarez scored twice in a 5-3 victory at Stoke City in the Premier League on Sunday to take his incredible tally to 22 goals in only 16 top-flight games.
The Merseyside club are fourth in the table, six points behind leaders Arsenal, and Suarez - the leading scorer in the Premier League - is confident they can bring Champions League football back to Anfield.
He told the club's official website: "It's very important because we know that in the last two years we haven't demonstrated that Liverpool can play in the Champions League.
"Now we are playing very well and we have the level to play in the Champions League. We have really good players and if we continue at this level, we can do it."
Suarez's sensational form has led to him being billed as one of best players in world football, but the former Ajax man is happy to reward his club and supporters for standing by him.
He added: "When you are a child, you imagine a lot. Now many people or players speak about that and it's unbelievable for me,
"And also for Liverpool, because in the last two or three years we have not played very well and not demonstrated our level. Now we are back to that.
"You work hard for the supporters and the people. It's important because the last few months were a little difficult for me. Now I've changed and it's okay."
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