Piquionne put the Hammers 2-1 up but was shown a second yellow card for celebrating with the supporters and Marouane Fellaini then grabbed a point against the 10 men.
"It wasn't great but we got a point. It didn't look as if we were going to get any near the end," said Moyes.
"When we got back to 1-1 I thought we would go on and get the second goal but unfortunately they got a second.
"When you go 2-1 down at home you go for it anyway but when we saw the sending-off it gave us a chance to attempt to throw the kitchen sink.
"Thankfully we got the equaliser and when it went to 2-2 I actually thought we could have used the last couple of minutes better than we did to try to get the winner."
Source: PA
Source: PA