The Reds moved back into the top four of the Barclays Premier League, where they have spent most of the season so far, after Sunday's 5-3 win at Stoke.
And Suarez - scorer of a brace in the game - feels things are looking good in terms of the Merseysiders' prospects of staying there and going on to make a return to the Champions League, in which they have not featured in since 2009.
The Uruguay international told Liverpoolfc.com: "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 double at the Britannia Stadium took him to 22 goals for the campaign - scored in only 16 league matches.
He missed Liverpool's first few fixtures this season as he completed the 10-game suspension he was serving for his infamous bite on Chelsea defender Branislav Ivanovic in April.
The 26-year-old frontman has been at the centre of various controversies during his career, but of late, the headlines about him have tended to be positive, with there being talk of him being among the best players in the world.
Suarez himself says he is a changed man and that the praise he is getting is "unbelievable".
But he has also stressed that his main concern is the progress of the Liverpool team.
He said: "When you are a child, you imagine a lot. Now many people or players speak about that and it's unbelievable for me.
"(It is) 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."
He added: "For my confidence, it's very good, but the most important thing is Liverpool. That's more important to me.
"The squad is playing very well; for the forwards, it's easier on the pitch.
"If I score or not, it's not important to me. It's more important that we win the game."