The FA brought the charge against the north-east club for the conduct of their players after referee Mark Halsey dismissed midfielder Didier Digard in the match.
An FA statement on their official website revealed Boro had admitted the charge at a regulatory commission hearing today, with £2,000 of the fine suspended until the end of the 2009/10 season pending any further breaches of the same rule.
Digard was shown a red card after 63 minutes of the match for a challenge on Borja Valero.
Boro were already trailing 2-0 at that point before going on to lose the match against their fellow relegation rivals 3-0 at The Hawthorns.
"At a regulatory commission hearing on Wednesday, Middlesbrough FC were fined £6,000 for failing to control their players," the FA statement read.
"The charge relates to the conduct of Middlesbrough players towards referee Mark Halsey following the sending-off of Didier Digard during the second half of their match against West Bromwich Albion on 17 January.
"Middlesbrough admitted the charge and requested a personal hearing, £2,000 of the fine is suspended until the end of the 2009/10 season pending any further breaches of the same rule."
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