Stevenson was issued with a notice of complaint by Scottish Football Association compliance officer Vincent Lunny on Monday for his challenge on Hibernian captain James McPake in the Edinburgh derby.
Hearts confirmed they would challenge the sanctions offered to the former Ipswich man for the tackle, which took place during the goalless draw at Tynecastle on January 3.
However, a fast track tribunal has upheld the compliance officer's reference and a ban has been imposed with immediate effect.
Stevenson will miss a Clydesdale Bank Premier League clash at Celtic Park and the Easter Road semi-final against Inverness on January 26.
Stevenson expressed his disappointment at the outcome, particularly sitting out the last four of the League Cup.
He told STV: "The ball was there to be won. I certainly didn't go in to do James McPake.
"It was two grown men going for a tackle. It's a man's game, but rules are harsher these days.
"I didn't think it warranted a two-match ban so I am disappointed.
"It's a massive blow to miss the semi-final because I have never played in one before."