Adam Johnson gave Poyet's team a 37th-minute lead but Paulinho struck to ensure it was all level going into half-time. However, John O'Shea's own goal five minutes into the second half means the Wearsiders remain rooted to the foot of the Barclays Premier League table, with the loss to Spurs their 11th in 15 outings this season.
Poyet said: "I'm very disappointed, for many reasons: one, because we don't have the heart to compete with Tottenham for long periods.
"To go ahead and score with a great goal, the type of goal we try to convince the players that they can do, but then something happened.
"Something can happen in the last minute, a simple foul, but the ball is played in and it drops and they are better than us, they are quicker than us. And once more an own goal, I don't know what to say about that. I have never seen it before.
"And then it was too open, you cannot play that way against Tottenham. You shouldn't be in that situation again."