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."
I know I'm just taking the p##s. I know its a strong last 8 in Champs League after Bayern getting through last night & that's the only consolation with us going out is that I don't think we would have won it with teams that are left. Will be interesting to see who Real get now. I had thought that with Barca losing 2 0 that this would be an great opportunity missed by United to win it but with them through I think if they play to their best they will win it. Bayern didn't look great last night but I think you will see a different bayern team in quarters, Dortmund are a strong side as well. Juve too. Plus Malaga have been the surprise package this year with Gala. Then PSG too who have spent a lot of money on players they're good side but it all depends on who they get if they get one of the top teams I think they will be gone.- keano81