Spurs head coach Nuno Espirito Santo took the blame for a 3-1 defeat, admitting he made "bad decisions" and his game plan "didn't work".
Arsenal raced into a three-goal lead inside 35 minutes through Emile Smith-Rowe, Pierre-Emerick Aubameyang and Bukayo Saka before Heung-min Son scored a late consolation towards the end of an improved Spurs second half.
The defeat has raised more questions about Nuno’s style and tactical acumen, and Lucas criticised the performance, saying Spurs were too direct and not aggressive enough at the Emirates.
"The feeling is very, very bad. We know what it means for the fans, for the club and of course we wanted to win, we wanted a different result," Lucas said.
"It's not a time to speak. It's a time to be quiet and work hard. It was a very bad game, it didn't work at all.
"I think they took advantage of our mistakes. We gave them too much space. And we didn't play. We didn't try to play. We didn't try to have the ball.
“ We have quality to have the ball, to build, to do more than what we did. So many long balls. We were not aggressive enough and they punished us.
"Even 3-0 down, it was not finished. Second half we did different, it was quite [good]. But it was too late, 3-0 from the first half was very difficult to turn over.
“But we tried, we fought until the end but it was not enough we're not happy and we need to improve.”
Despite a third London derby defeat on the bounce and the first time since 2003 Spurs have conceded three or more times in three consecutive matches, Lucas called for calm.
"We need to run more. We need to be more aggressive, we need to work more, work harder,” he said.
“But we cannot be crazy. It's only the beginning of the season. We have a lot of games to play so we need to improve as soon as possible.
"It's Premier League. Every game is hard, every game is a war. The first three games was good, especially against [Manchester] City. I don't know why we changed our mind against [Crystal] Palace, it didn't work.
“We didn't know how to react after but we need to react as soon as possible. We need to improve. Like I said, we have the quality to do better.
"We need to know how to pass this moment, how to face this moment. We're all good players who have quality to improve. To do better. That's the Premier League, that's football."