"What disappoints me more is that the confidence we have gained from our away-performance results was there for all to see in the first half," Allardyce told Sky Sports News.
"I expected that one of the things we'd been short of was getting the first goal and going ahead, and I thought once we got that the lads were going to be as good as they've been all season - having conceded one goal away from home from a penalty that shouldn't have actually been a penalty.
"But then our own errors and our own mistakes have let Norwich back into a game that they shouldn't have got back into and we've ended up with no points instead of picking up points and a win. We've only ourselves to blame."
West Ham are currently 16th in the league table with 10 points from 11 matches.