City's run of five successive league wins without conceding came to an abrupt halt as Victor Moses and Diafra Sakho set up a 2-1 win the for the Hammers at the Etihad Stadium.
Club record signing Kevin de Bruyne pulled one back before the hosts went on to dominate the second half, but they could not find a way past inspired goalkeeper Adrian.
It was a second defeat for City in the space of four days after losing to Juventus in the Champions League in midweek.
Pellegrini said: "It was frustrating because I think they were three very important points here at home.
"We conceded two easy goals and that maybe was one of the reasons why we didn't win.
"In the last two games, we didn't play with the concentration and intensity we need in defending.
"Juventus shot twice at our goal and they scored two goals
Today it was exactly the same
One shot at the edge of the box and one corner were all the offensive volume West Ham had in the whole game.
"We must concentrate more because two balls decided the result."
City had to make a late change to the side after playmaker David Silva withdrew before kick-off.
Pellegrini said: "I don't want to have the excuse of David Silva why we didn't win
I don't think there was one player that would change the story.
"David had a kick in his calf and he tried in the warm-up but he felt his muscle was stiff so he didn't play."
Pellegrini, who added that defender Eliaquim Mangala was taken off at half-time with a muscle injury, dismissed suggestions his team may have been over-confident.
He said: "We never believed that because we won five games we were the champions of the Premier League.
"We have to play 32 games more, 96 points to play for, so nobody can believe that."
For West Ham, the result represented another notable away scalp under new boss Slaven Bilic after also winning at Arsenal and Liverpool.
Bilic said: "It is a surprise, let's be honest
This game was different from Emirates and Anfield
With the greatest respect to Liverpool and Arsenal, this team (City) are the best in the league.
"We knew we would have to score goals to get something, we knew we would have to run like crazy, and we knew would have to be lucky
It is very difficult, if not impossible, to stop them for 90 minutes but we have done it.
"We didn't nick it
It would have been fair if they equalised, but we also had chances.
"That is why I am so proud of our performance
The guys have done brilliantly, not only fighting-wise but also playing-wise."
The Hammers now have 12 points from their six games, just three less than leaders City, but Bilic is not getting carried away.
He said: "There is a tiny line between confidence and arrogance or confidence and laziness.
"It is hard not to get carried away a little but that is also part of my job to install in their heads that we are good, but that you have to know what to do to stay good.
"There are going to be ups and downs, we are not Real Madrid, but it is looking very good now."
Source : PA
Source: PA