The forward's wonderful free kick was not enough to secure all three points for Slaven Bilic's side.
The Hammers were held to a 1-1 draw, with a Rickie Lambert deflected effort levelling the scores after Zarate had put the home side into the lead with an excellent free-kick.
It was a disappointing afternoon for Slaven Bilic’s side, who dominated the possession and created most of the chances in the game.
Zarate though, says they didn’t do enough to secure all three points on Sunday afternoon.
“We didn’t feel so good with the result,” he told whufc.com.
“We worked for the three points, and thought all week about taking them - doing the pressing, doing a good job, but it wasn't enough today.”
"I practice the free-kicks every day, in every training session with Rapha [Spiegel] or Adrian. It's a good way to score and to give a goal for the team."
The failure to secure all three points on Sunday is likely to be a big blow to the Hammer’s top four hopes.
A win would have seen them move to within three points of Arsenal, who currently occupy fourth place in the table, after their draw with Norwich.
Instead, they are now eighth in table and five points away from their London rivals.
The table is tight to say the least though, with Liverpool in sixth only one point ahead of the Hammers and Tottenham just three points away in fifth, meaning there is much still to play for.