Netherlands international Blind got a mis-firing United forward line out of jail when he fired home an equaliser two minutes into stoppage time, cancelling out Cheikhou Kouyate's superb 49th-minute opener.
The midfielder conceded that Louis van Gaal's team struggled to combat a battling West Ham side, especially during a frustrating goalless first half at Upton Park.
"It’s a reward for not giving up but of course you want more," Blind told Sky Sports.
"The first half was a real battle. We couldn't really play the ball how we want, we couldn't play possession.
"The second half we started well but then they got the early goal and after that we had to fight again for the good moments.
"I think we picked it up well and showed we are capable of fighting but, of course, we are not happy with the draw."
Kouyate twice flicked the ball up for himself and volleyed home on the turn after the visitors failed to clear a Mark Noble free-kick, one of numerous occasions on Sunday when Van Gaal's men struggled under West Ham's set-piece threat.
Blind acknowledged that the physical edge to the hosts' game posed persistent problems.
"Especially [in the] first half, they were winning a lot," he added. "In the second half we did it better, winning some second balls and creating some danger from that.
"We could have done more to win the second balls but they have strong strikers and strong midfielders - it’s difficult."
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