The London club were consigned to a 9-0 aggregate defeat in the League Cup semi-final as Manuel Pellegrini's free-scoring side recorded a 3-0 win in the second leg at Upton Park on Tuesday night.
West Ham's hopes of reaching the final had already been effectively ended by a humiliating 6-0 defeat at the Etihad Stadium in the first leg, when some dreadful defending proved to be costly.
City capitalised on the Premier League strugglers' frailties at the back again in the second meeting, with Alvaro Negredo scoring twice and Sergio Aguero also on target.
Each of the three goals were easily avoidable and Allardyce warned his players they can ill afford to make life so easy for opponents as they battle to avoid relegation from the top flight.
He said: "We've had more clean sheets away than at home, so that becomes an ultimate problem that we've got to do better.
"We've got to protect our goal better and, while that might be harsh in this game, it's about making sure we make teams work much harder for the goals that they score.
"Ultimately, if you give a team like this the chances we gave them, then they are going to punish you and they did. We did create chances, but once you lose the ball you've got to get back in and be defensively sound.
"In more games coming up, when we play teams of lesser ability than Man City, that's going to be even more important - getting the attacking side of it going and the defensive side right. We made two errors for two of their goals on Tuesday.
"City have scored 19 goals and conceded one to get to the final, which shows you the quality of their team, but I was a little disappointed with the way we conceded the goals."
There was more concern for Allardyce when Mohamed Diame was carried off with what appeared to be a serious knee injury and Joe Cole was also withdrawn.
The duo will be assessed, but Allardyce is hopeful that neither player will face a lengthy spell on the sidelines.
He said: "Obviously we were disappointed to lose Joe Cole and Mo Diame to injuries, but we'll have to see how serious they are. I spoke to Mo afterwards and it seems it might not have been as serious as it first looked."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
