The Brazilian-born Croatian was given the ban on Tuesday after UEFA's disciplinary and control panel ruled he had tried to deceive referee Manuel Enrique Mejuto Gonzalez during last week's play-off round second-leg tie against the Scottish side.
UEFA ruled he went down in the penalty area at the Emirates Stadium despite there appearing to be no contact with goalkeeper Artur Boruc, with Eduardo converting the spot-kick himself to give Arsenal a 1-0 lead on the night in a 5-1 aggregate win.
"We have been informed that we will receive a 'reasoned decision' from UEFA by Thursday of this week. Once we receive UEFA's rationale, we will make a decision on the next steps," Arsenal said in a statement on their website.
"We have been deeply frustrated by the perfunctory and apparently arbitrary process that UEFA has followed in this instance."
The suspension means Eduardo will miss the team's opening Group H matches against Standard Liege on September 16 and Olympiakos two weeks later and Arsenal have three days in which to lodge an appeal against the decision.
"We believe it is imperative that UEFA's explanation for its decision provides clear and comprehensive standards that will be consistently enforced," the statement continued.
"It is also critical that UEFA provides specific details of the processes it plans to adopt in reviewing all games under its jurisdiction."
Arsenal manager Arsene Wenger accused European soccer's governing body of waging a "witch-hunt".
"I find it a complete disgrace and unacceptable," the French coach said after Eduardo was charged.
"We won't accept the way we have been treated in this case for two reasons. I believe that you can debate whether it was a penalty or not. For me it's a witch-hunt that we see and not an objective judgement of a case."
