Sam Allardyce admitted he was "bitterly disappointed" to see his side once again let a result slip out of their hands at the Boleyn Ground.
The unchanged Hammers looked on course for a third straight win when Leeds United were able to break and make it 2-2 with just seconds remaining in normal time. It was hard to take, following on from the 1-0 defeat at home on the opening day by Cardiff City.
An early Carlton Cole strike, his second goal in as many starts, was cancelled out in the second half by Ross McCormack on the hour before a Patrick Kisnorbo own goal three minutes later restored the home advantage. Then, just as it looked like the Hammers, featuring John Carew as a second-half substitute, would hang on, Leeds equalised again through Adam Clayton's smash and grab raid.
Allardyce said: "We are bitterly disappointed because we came through the ebb and flow of a game where the quality had been very good. Both sides were trying to create on the attacking side, it ebbed and flowed.
"When Leeds had a good spell then we had to dig in. We overcame that and took control of the game again by making the substitutions we did. That got us back to 2-1 and we always looked likely to win the game maybe 3-1.
"We missed the chances and then right at the dying embers, instead of keeping the ball in the opposition half we needlessly gave it away."
Allardyce was frustrated by seeing two first half penalty shouts turned down for apparent fouls on James Tomkins and Carlton Cole, while relieved to see Leeds star turn Max Gradel, a constant menace to the Hammers rearguard, miss from the spot for Leeds after a Matt Taylor handball.
While Robert Snodgrass hit the woodwork on 13 minutes, Scott Parker was similarly denied on 76 minutes before Kevin Nolan somehow missed from close range in the 89th minute
Barely 60 seconds later, the manager and the 28,252 at the Boleyn were dismayed to witness another late lapse at the end of what had been a tremendous week with wins at Doncaster Rovers and Watford.
"Of course Leeds are going to throw men forward and we have thrown two points away," Allardyce summed up. "It makes life very difficult for us because we have to go and make it up away from home next weekend. We have really got to make this place somewhere we enjoy playing, rather than being disappointed."