The Uruguay striker hailed the Anfield club's supporters as crucial to his rehabilitation after the ban for biting Chelsea defender Branislav Ivanovic.
But the 26-year-old said a rhinoceros hide formed during a troubled childhood in his native Uruguay have helped him overcome a string of controversies in European football.
Suarez admitted his Liverpool career would have been over had the supporters not welcomed him back into the Anfield fold.
The Salto-born forward collected the 2013 Player of the Year award at Monday's William Hill Football Supporters' Federation Awards at Arsenal's Emirates Stadium.
He said: "When I was a child I had too many problems, but I could try my best on the pitch.
"Once I was playing football I could try my best, because I just love to play football, I play with my heart."
Thanking the Liverpool faithful for warming to him again this season, Suarez rated "coming back to play at Anfield" as his 2013 highlight.
He said: "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 will face a host of Liverpool team-mates when his Uruguay side take on England in World Cup 2014 in Brazil.
After the World Cup draw, Suarez revealed Steven Gerrard texted joking that England were "lucky" to face Uruguay.
Banter aside, Suarez knows how tough it will be to reach the knockout stages of the summer extravaganza.
He said: "Before the draw I hoped we would not face England.
"But when it said we would face England it was unbelievable for me.
"Stevie sent a message to me saying 'we are so lucky', and we were laughing because it's so funny.
"But now we are concentrating on the league and Liverpool.
"I think it's more difficult at the World Cup, it will be very, very difficult.
"Italy, Uruguay, England: they all have good players.
"But I think in the World Cup if you want to win, then in every game you must concentrate, and you must focus against every country."