The Uruguay international scooped the 2013 Player of the Year award at the William Hill Football Supporters' Federation Awards on Monday night.
After receiving the honour at Emirates Stadium, former Arsenal target Suarez said Liverpool will know by January whether they can fight for a top-four finish, and maybe even challenge for the title.
Suarez missed the first six matches of the season due to the ban he received in April for biting Chelsea's Branislav Ivanovic, but has hit 17 league goals since returning to action, including two in Sunday's 5-0 romp at Tottenham.
Brendan Rodgers' side face Cardiff, Manchester City and Chelsea before the turn of the year, and Suarez has admitted that run will test the Reds' title mettle.
"I think it's too early to say," said the 26-year-old when discussing Liverpool's Premier League chances.
"If we continue this level the next two or three weeks we can win the league or we can finish in the top four.
"It's important we concentrate and focus on the next game. We know that after Cardiff we have two very, very big games.
"That will be important to what comes next."
Suarez paid tribute to Liverpool's supporters for their faith after his biting ban, admitting he would not have had a future at the club without such backing.
And he claimed that winning over the Liverpool fans after his "difficult year" has been his personal highlight of 2013.
He added: "Coming back to play at Anfield: because after so many difficult moments for me I was able to win the supporters back, and that was unbelievable when I came back to play.
"They helped me, and that was important for me, for my confidence, and for my family, because they are together with me in this.
"It's very special for me (the award) because my hard work on the pitch is recognised.
"Everybody knows about my problems and my difficult year, but after that I forgot everything and have been able to get back on the pitch.
"Liverpool are starting to reach their potential and we can play our best on the pitch.
"It's very important that we stay together, we keep going, this is very important.
"If Liverpool don't have these players I cannot continue my level, because it's too much.
"They know I am important, so they try everything to stay together, that's important for me, but it's more important for the club."
Suarez captained Liverpool for the first time in Sunday's Tottenham rout, but the striker knows Steven Gerrard will reclaim the armband when he returns from injury.
He said: "I was a little surprised by that (the captaincy call), but I think we have only one captain here, Steven Gerrard.
"If we stay together, we are together, we are the captain, the team is the captain, that's important.
"It's far more important than me being captain that we win 5-0 against Tottenham, this is very important."