The Uruguay forward took his goal tally to 22 for the campaign with the opener in Wednesday's 2-2 draw at Arsenal.
The often controversial Suarez has quickly become a cult hero on The Kop since his £22.8million move from Ajax on transfer deadline day two years ago.
The 26-year-old intends to continue to drive the Reds on as they look to develop into Champions League challengers once again under Brendan Rodgers.
"I hope [to be at Liverpool] for a very long time because it's a massive club that kids dream about playing for," Suarez told the club's official website, www.liverpoolfc.com.
"I've been very proud to be at a club like Liverpool and to have made the decision to come here.
"In two years I've lived through some spectacular and very special moments that I will never, ever forget.
"There have been a few difficult times as well, but with the support of my family, the club and the fans, things have gone well for me."
Suarez continued: "I do feel at home here. When I'm out and about, all I get is support and encouragement from the local people and that's very important and when I come here to the club I feel like people have known me all my life.
"I hope to be able to help out the team for as long as I possibly can while trying do something to make the club and the fans very happy."
Liverpool had taken a commanding 2-0 lead at Emirates Stadium, with Jordan Henderson doubling their advantage on the hour following more poor defending from the hosts.
However, the Gunners showed their undoubted attacking prowess by fighting back to level through Olivier Giroud and a blistering strike by England forward Theo Walcott.
Reds defender Lucas feels the team provided the needed response from their FA Cup humiliation at Oldham on Sunday, even if they could not see the game through.
"We responded really well from the FA Cup defeat against Oldham. We showed the right mentality and a good attitude," Lucas told reporters.
"This was a really important game for us. Arsenal are only three points above us and this was an opportunity to go level with them, but we know how hard it is to come here because Arsenal pass the ball well and move the ball quickly.
"I think we were defending really well but in the space of 10 minutes we conceded two goals and the game changed.
"It would have been a big three points for us but we just couldn't get them."