Pellegrini was at a loss to explain how his team failed to hold on for three Barclays Premier League points after twice leading at Villa Park.
City dominated the first half and deservedly led through Yaya Toure's sixth goal of the season just before the interval.
Pellegrini said: "Of course it is disappointing because I think we played very well in this game.
"From the beginning we had possession of the ball, we had the chances and we didn't have any risk in our own goals.
"It is unbelievable we didn't win this match but football has these things. The team that deserves to win doesn't always win."
It was yet another frustrating away day for title hopefuls City after losing at Cardiff last month and a goalless draw at Stoke a fortnight ago.
It seemed City had found their feet after last week's stunning derby destruction of Manchester United but they clearly still have vulnerabilities.
El Ahmadi was fortunate not to be flagged offside before the opening goal but the foul outside the area for Bacuna's free-kick strike was needlessly conceded.
Weimann's goal then came in frustrating circumstances as the Austrian ran unchecked onto a long kick from goalkeeper Brad Guzan.
Pellegrini said: "I think the first goal was offside, the second goal was a free-kick and the third goal was unbelievable.
"Maybe drawing 2-2, at that moment, made the players go forward and we left a gap. They had the ball with the goalkeeper and then a chance to score in our goal.
"In five minutes we threw away all the work we did in the whole match.
"For the moment we haven't had a victory away. The other two games were very different, against Cardiff and Stoke.
"I thought the team played the way we need to play and the way I want to play here. I can't believe we didn't win."
Pellegrini has no doubt City will recover to play a prominent role in the title race.
He said: "We are not thinking about the title at the moment. We are thinking about winning the most amount of matches.
"In the Premier League, the difference (between teams) is very small.
"If we play the way we are playing I am absolutely sure we are going to be fighting for the league."
Even though his team were outplayed for most of the first half, Villa boss Paul Lambert had no doubt they could fight back.
He said: "I know they had a lot of possession but Guzan didn't really have a save, as such.
"They are one of the favourites to win the Premier League, and one of the teams that could win the Champions League.
"That shows the magnitude of this result. They might have rested a few for the Bayern game but, if you look at the side, they were a lot of top players.
"It is a big win, three points for us. I am delighted to win."
Lambert, whose side survived a relegation scare last season, was unwilling to say whether it was his best result since taking charge at Villa last year.
He said: "There have been (other) big games and big results, big moments at certain times.
"But this is a fabulous achievement because of the magnitude of their club and the players they have got.
"Where I will say it was very pleasing is that we had to come back twice. We have made a really good start in the league.
"We have played Arsenal, Chelsea, Liverpool, then Tottenham in the cup, and then Manchester City.
"It has been one hell of a start but we have come through it and are playing with a lot of confidence."
- Sports & Recreation
- Barclays Premier League
- Karim El Ahmadi
- Manchester City