Nathaniel Clyne's cross appeared to hit the arm of Villa defender Ryan Bertrand 10 minutes from time in Saturday's goalless Premier League stalemate.
Referee Lee Mason decided not to award a spot-kick, though, as Southampton were made to rue a disappointing afternoon of missed chances at Villa Park.
Rickie Lambert, Steven Davis and Adam Lallana all wasted good opportunities for the visitors and Pochettino was unhappy with Mason's controversial decision.
"It was a clear penalty," Pochettino said.
"You (media) all probably had a better view from the TV but from my point of view it was a clear penalty and the linesman as well was quite close. I really don't know.
"It's unexplainable to me, why that penalty was not given.
"We feel hard done by because in the last few games, we (have) had decisions that haven't gone our way. Probably if those decisions had gone our way, as they should have, then we would have more points right now.
"The players do not deserve the calls that they haven't been given because they should have been given. Right now we would be higher in the table if those decisions had gone our way."
Pochettino bemoaned his side's profligacy in front of goal as Southampton's winless run extended to three games.
But he was happy with their performance against a struggling Villa side.
"I think we deserved to win," he added.
"I think we did everything right, we did everything well except actually score. I'm very happy with the team's performance but I'm a little bit sad because we created many chances…but I think we were a little wasteful as well with the chances that we created.
"We're playing really well but we need to be more clinical in front of goal. That's what we've been lacking these last few games."
Pochettino also swerved questions about his future, declaring that it was "not the moment" to discuss the issue, but added that he still had one year remaining on his Southampton contract.
