Lucas still had a further two years to run on the contract he signed in
"If I didn't believe, I don't think I would have signed a new deal," he said.
"I think that's why we've seen a lot of players signing new deals – because we really believe this club will be back where it should be.
"The last two or three years have had some difficult moments for the club but I think keeping these players and getting help from new players will be important for us.
"And we'll work really hard to do whatever we can to put Liverpool back fighting for titles and in games the fans are really looking forward to.
"When I retire I would like to look back and see that my career at Liverpool has been a successful one.
"That means winning – and I still believe we can win important things here.
"Maybe it hasn't been as quick as I or everybody would have wanted but I am sure in a few years' time we will be celebrating some important titles."
Lucas is confident that despite an up and down first season in charge, manager
"Brendan played a big part in my new deal," he told liverpoolfc.com.
"I spoke with him a few times before we agreed the new contract. "He has been a very good manager for all of us and we're really looking forward to next season.
"We know how he works and how he wants us to play and everyone is looking forward to having a better season.
"I am really delighted to have the opportunity to play for this club.
"It's where I think I belong and where I wanted to stay.
"It was an easy decision because after the long period of my career I have had here I think I would like to give the best of my time to this club.
"It was not a difficult decision to make and I am really looking forward to what will hopefully be a few more years with a lot of success."