Clattenburg awarded a second-minute penalty to West Ham, who went on to win 2-1 against the Canaries at Upton Park on New Year's Day, for shirt-pulling by Ryan Bennett on Winston Reid.
Snodgrass, 25, later tweeted: "The referee kills the game. If that's a pen you will need to give 100 pens a season, small decisions change games."
The FA confirmed there will be no action against Snodgrass - players and managers can criticise refereeing decisions so long as they do not imply any bias.
The FA's social media rules state action may be taken for "comments about match officials which imply bias, attack the officials' integrity or which are personally offensive in nature".
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