Boss Sam Allardyce was full of praise for the display from his players but was ultimately left frustrated at Ewood Park.
Rovers fell behind in dubious circumstances when Mark Noble netted for the visitors on 35 minutes, but Luis Boa Morte had been in an offside position in the build-up for the goal and it shouldn't have stood.
The second half was all one way traffic towards the Blackburn End and after substitute Keith Andrews had fired Rovers level five minutes after the restart there was only going to be one winner.
But Rovers just couldn't find a way past a resolute West Ham defence, a frustrated Allardyce having to settle for a point.
"I think that I have a tremendously disappointed group of players and staff in the dressing room," said Allardyce on Radio Rovers after the game. "I think that it was a great performance.
"I think that in the first half we were very unfortunate to come in one-nil down as we knew at half-time that their goal was an offside goal as Boa Morte was offside when the ball was played through.
"The assistant referee was in the correct position not to miss it and has.
"But after that kick in the teeth we saw a wonderful second half performance of persistent, constant quality and pressure into West Ham's goal.
"Whatever we did, whether it was a great piece of play, or winning a knockdown, it kept hitting a West Ham player and deflecting the wrong way, and never deflected the right way. And then when we scored it was offside and we had two of those.
"We continued to pepper the goal for 45 minutes constantly, and normally under those circumstances after a great goal from Keith Andrews we haven't found ourselves with the three points we deserved today and that is a real blow.
"We didn't find the clinical finish to win it, but unfortunately one of the decisions that is out of our hands has gone very very much against us today and has now, looking back on it, has perhaps cost us two points.
"But I have to give a huge amount of credit to the lads for the way they have performed today.
"What can I say to the players today apart from lads I can't believe how unlucky you've been today, I can't believe that you haven't won this game. But you've got to keep the belief that performances like this will win you more than you'll draw.
"It is another point towards the total but it is unfortunately disappointing for us today that we haven't got the three"
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