The Hammers faced a depleted Arsenal side following the first half dismissal of Thomas Vermaelen, but failed to capitalise from the penalty spot before Cesc Fabregas's late strike dealt Zola's side a crushing blow in their bid for Premier League survival.
"I thought the first half we played our best game of the season," Zola told ESPN. "We certainly deserved something more."
Alessandro Diamanti had the chance to level the game with a penalty prior to the break, but his shot was well saved by Manuel Almunia, who had little to contend with in the second half.
"In the second half I wanted a play a little more, play left to right and create space in the middle," added Zola. "But we lost a little bit of discipline and conceded the second goal - I'm disappointed as it was a very big opportunity for us.
"Today, in the first half I saw some very good football - the whole team was excellent.
"In the second half we wanted to resolve the game as individuals rather than as a team, that's the disappointing thing for me."
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