The sanctions were imposed by UEFA after he picked up a red card in a Champions League qualifier against Malmo on August 3.
The Scottish champions felt the punishment was excessive but the appeal was dismissed on Monday by UEFA's Appeals Body after hearing the case in Switzerland.
Whittaker was dismissed for throwing the ball at opponent Jimmy Durmaz as Rangers were held to a 1-1 draw on the night in Sweden and crashed out of the competition 2-1 on aggregate.
The versatile player, who has not played since that game with a broken toe, will miss this Thursday's Europa League play-off second leg against Maribor at Ibrox regardless of his fitness, as well as the club's next European tie.
Monday's decision has been described as "disappointing" and "unfair" by Rangers, who believe his red card while playing for Scotland against Spain in October 2010 was taken into account when hearing the appeal.
A statement on the club's official website said: "Rangers have been disappointed to learn UEFA has upheld their three-match ban imposed on Steven Whittaker for his sending off against Malmo in the Champions League on August 3.
"The club appealed the original decision as it felt a punishment of three matches was excessive but UEFA's Appeals Body heard the case in Switzerland this afternoon and dismissed it.
"The club understands Whittaker's sending off for Scotland in a match against Spain at Hampden in October 2010 - for two yellow card offences - was also taken into account today.
"Rangers find this disappointing and believe it is unfair as the player has enjoyed a good disciplinary record throughout his career with Hibernian at Ibrox and with the national side."