The Hammers were 2-0 down in their Europa League quarter final tie with Bayer Leverkusen after the first leg.
Despite taking an early lead in the second at home, they ended up drawing 1-1 on the night and went out 3-1 on aggregate.
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Post-game, Moyes stated: The team did brilliantly.
They were fantastic and they deserve all the plaudits for their performance. They were magnificent from the start to the end.
We couldn't quite keep the energy up as much in the second half, but great credit to them."
He added on the early goal: We'd earned the right to score the first goal.
If anything, we should probably have scored three in the first half and we didn't take the chances when we should have done.
That was probably the biggest reason why we didn't get it."