The Hammers boss said he was disappointed with the way his side conceded against Manuel Pellegrini's men but praised their response after going two goals down
City claimed their first away win of the Premier League season at Upton Park, as two goals from Sergio Aguero and a late David Silva effort helped them to victory.
The win lifted last season's runners-up to fourth in the table but Allardyce felt his side made it easier for City by making silly mistakes at the back.
Aguero's first goal came after a Fernandinho ball was allowed to run into the penalty area while the Argentina striker's second was a free header from a corner.
"I think that we came out of the traps and thought that we could set the tempo but I think what happened is that Manchester City decided they would with the quality of players they have," Allardyce told reporters.
"When you have the front two [Aguero and Alvaro Negredo] and Yaya Toure and [David] Silva passing the ball like they pass it, it frightened us a little bit and puts on the back foot.
"But then we made two basic errors for their two goals rather than the quality of Aguero or Negredo or Silva putting the ball in the back of the net with great fluent moves.
"A simple ball down the middle for the first goal and somebody not picking up the smallest Man City player up on the second goal was really disappointing for us."
Allardyce was pleased with his side's response to going two goals down though, as Ricardo Vaz Te's bicycle kick set up a tense finish.
West Ham pressed on and threatened to score an equaliser before Silva's cultured effort in the dying stages.
"We gave it a go. I was at least pleased with the response the lads showed, not giving up, fighting right until the end," he said.
"Of course when we got to 2-1 with a good goal, we showed a little bit more of our passing qualities, which failed us in the first half.
"But our only real contribution from an attacking point of view was about 20-25 minutes and that was after Manchester City were already 2-0 up. That was too late."