Pochettino demands cutting edge from Spurs
Pochettino's predecessor Tim Sherwood watched as his Villa side claimed maximum points, with Christian Benteke heading home the only goal of the game 10 minutes before half-time.
However, the hosts struggled to create attacking openings - their best coming through a Harry Kane strike that clipped the roof of the net.
Even the late dismissal of Carlos Sanchez failed to allow Spurs back in, with Pochettino frustrated by a lack of poise up front.
Asked by BBC Sport whether his side deserved anything from the game, he responded: "Maybe, when you analyse the 90 minutes, maybe yes.
"We had chances, possession of the ball, managed the game but the first chance they had, they scored.
"Then it was difficult for us. I'm disappointed with the result, disappointed for the players, it was not a good game.
"We need to increase our performance if we want to take the points, we need to be more clinical in offensive situations.
"I think maybe we deserved more in this game but the feeling wasn't good today and we need to improve."