Despite it being a positive performance, there was a feeling of disappointment surrounding Tottenham on Sunday.
Tottenham conceded to former winger Aaron Lennon in the 22nd minute before Dele Alli replied with a delightful turn and volley on the stroke of half-time but Pochettino felt it was a missed opportunity for his fourth-placed side.
"We dropped two points. The first half I think was fantastic, one of our best performances so far," he said.
"In the second half we managed the game until around 75 minutes, when I think Everton increased their level.
"I think we need to feel proud, and our performance was really good - but we are disappointed with the final result. We believe in the way we play, we are very ambitious and the players are very disappointed in the changing room.
"Always at the end of the game we play some music but today (Sunday) we [did not, because we] are very disappointed, because the feeling is that we dropped two points."