The Reds boosted their slim hopes of a top four finish with a thrilling 3-2 win over third-placed Tottenham on Sunday.
Liverpool find themselves seven points behind fourth-placed Chelsea with nine games remaining in the Premier League campaign.
Brendan Rodgers is ignoring all talk of a possible top four finish, but Lucas feels the battling win over Tottenham shows they are improving.
"Our biggest virtue in this match was that we never stopped fighting. We didn't get upset at losing and showed our strength to come back," Lucas told Terra.
"We are improving at the right time and, because of that, we can dream of a Champions League place.
"It was our third consecutive victory, something that is worth a lot given the difficulty of the Premier League. We will continue to work hard, without fanfare, and things will come naturally."
Lucas also praised Rodgers for setting the team out to combat Spurs dangerman Gareth Bale.
"We knew most of Tottenham's plays would be via Gareth Bale, it's always hard to mark him, but our manager Brendan Rogers set up the team well and we did our job.
"We had some challenges during the game and thank God I did well. As I said, this win made me very happy and made us sure we are on the right path."