Despite dominating for long periods, the visitors had to wait until the final minute of the first half to go in front when in-form midfielder Yaya Toure netted his sixth goal in eight games.
Karim El Ahmadi got the benefit of a questionable offside call to haul Villa level early in the second period before Edin Dzeko, so often profligate throughout the afternoon, glanced home a Samir Nasri corner to restore City's advantage in the 56th minute.
But from there the wheels came careering off for Pellegrini’s men as first goalkeeper Joe Hart was rooted to the spot as Leandro Bacuna crashed home a spectacular free-kick and then Weimann got the better of Matija Nastasic to prod Brad Guzan’s long clearance home.
"Of course I am disappointed because I thought we played very well in this game," said Pellegrini, whose side would have topped the Premier League table with a win.
"From the beginning we had the possession of the ball, we had the chances, we didn't have any risk in (front of) our own goal so it is unbelievable that we didn't win this match.
"I think the first goal is offside, the second goal was a free-kick and the third goal was unbelievable, maybe because drawing 2-2 at that moment made the players go forward and leave a ball from their goalkeeper where they have a chance to score in our goal.
"In those five minutes we threw away all that we did in the whole match."
"It (losing) is not only (frustrating because of) the table – we played really well today," he added.
"At the moment we haven't had a victory away but the other two games were very different against Cardiff and against Stoke.
"Today I saw the team playing the way we need to play and the way I want to play, so (it is) unbelievable that we didn't win."
