Spurs slipped to a shock defeat against Brighton last week and failed to bounce back in their bid to finish in the top four.
Spurs drop to fifth place and two points behind Arsenal in the top four race with five matches remaining for both teams.
Brentford dominated the first half and were unlucky not to lead at the break after Ivan Toney struck the bar with a header early on.
Spurs failed to find their rhythm before the break with Harry Kane's speculative lob the closest they came to a goal.
Christian Eriksen, who was playing his first match against his former club since returning to the Premier League, saw his deflected shot go wide after the hour mark.
Brentford went close again after 66 minutes but Kane managed to clear Pontus Jansson's header off the line.
Both teams had chances to win the game in stoppage-time but Toney's header struck the woodwork again before Kane's bicycle kick went just wide.
"We know what's at stake. I think in the last three games a lot changed and in the next three a lot can change," Tottenham defender Eric Dier said of the top-four battle.
"We need to focus on ourselves and try to win all of our games. Today is a hiccup but we have no time to feel sorry for ourselves. We have to go again next weekend. It's still in our hands because we have to play Arsenal."