Ravel Morrison's first-half goal had given West Ham a deserved half-time advantage against Chris Hughton's struggling side at Carrow Road on Saturday.
But veteran goalkeeper Jaaskelainen gifted Norwich an equaliser nine minutes into the second half when he dropped the ball and then upended Gary Hooper as he attempted to reclaim it.
Hooper converted the resulting penalty and Norwich went on to secure three precious points courtesy of a fine Robert Snodgrass free-kick and a stoppage-time strike from Leroy Fer.
West Ham had only conceded one goal away from Upton Park in the top flight before the game, and Allardyce cut a frustrated figure after a defeat that saw them drop below Norwich into 16th place - just a point above the relegation zone.
Allardyce told Sky Sports: "We let Norwich back into a game that we shouldn't have let them into. We've only got ourselves to blame.
"What I'm disappointed about is the confidence we've gained from our away results this year was there for all to see in the first half. We'd only conceded one goal away from home and that shouldn't have been a goal.
"We capitulated from our own errors and let Norwich back into a game that we shouldn't have let them into. We've only got ourselves to blame.
"I didn't expect that error from Jussi and the error for the second goal. It was such an unusual error and big error from Jussi, the players looked round and I think it killed them."
