The Reds’ Premier League campaign kicked-off with a lacklustre performance, with Spurs taking full advantage.
And Lucas says the Reds must step up their game by Wednesday’s home clash against Stoke City at Anfield.
“We are very disappointed. We came here looking for a good result, but Tottenham played really well,” the Brazilian told the club’s official web site.
“The first half wasn’t good for us and they pressed us really hard. I think if we had kept better possession of the ball it could have been key for us.
“We were better in the second half – we created some chances and could have had a penalty towards the end.
“Although we are disappointed, we now have to look forward to our next two matches at home and hope to take six points.
“We have to improve, we know that. Now we have two matches at home and we know we have to be stronger, especially for our fans.
“We have to try and beat Stoke and afterwards we can think about the next game with Aston Villa. We want to take six points.”