"We have asked to speak to people in authority at the Football Association to let them know how inconsistent we think the commission has been," Boro's chief executive told Sky Sports News.
"Our real feelings are for Jeremie, who through Middlesbrough's actions has received a larger ban for actions that weren't his but the club's.
"We are angry and we are dismayed over the whole thing, the benchmark is that the referee has made an obvious and wrong decision.
"We spent all weekend looking at the video, we also listened to TV pundits, journalists and others in football including members of the Premier League and Football Association and eventually we decided there were grounds for the commission to reconsider that and we accept that the commission can decide, as they have done, that our appeal fails but what we can't accept is that our appeal is frivolous - it was anything but that, it was well thought out and considered and that is where our anger is.
"The referee said he saw the whole incident, in his opinion Mascherano did nothing wrong and didn't warrant any further action, but if one player's action didn't warrant any action - why should the other? And that was our basis for the appeal.
"When Chelsea appealed against Michael Essien's ban for striking an opponent the commission decided the ban would stand, but didn't consider it frivolous - so I don't know what benchmark they used."