He said because of the lack of tickets sold there was no monetary loss for unsuspecting buyers, no financial gain for the brothers and no breach of trust, which made sentencing difficult.
Demissie and Asgedom had given the names of members in their soccer teams to the overseas operation so the tickets could be ordered.
The men were also sentenced to 200 hours of community work.
The Court of Appeal, in July, dismissed both a challenge to their convictions and Demissie's contest of the sentence he received.
The pair then both sought leave to take the case to the Supreme Court, which today refused to take their appeals.
The brothers attempted to raise issues about the indictment in their case, including that it was amended part way through their trial.
However, Justices Susan Glazebrook, Terence Arnold and Ellen France did not believe the pair were prejudiced by this.
The judges also did not believe the issues raised in the proposed appeal were of "general or public importance".
"Nor do we see any risk of a substantial miscarriage of justice in the particular circumstances of the case," they said.
On Demissie's sentence challenge, the judges said that the Supreme Court "rarely entertains" appeals of that kind.
"In any event, we agree with the Court of Appeal's conclusion that there is no basis on which the sentence could be described as manifestly excessive - if anything, it was lenient.
"In the result, we do not consider that it is necessary in the interests of justice that we hear and determine these appeals. They raise no point of general or public importance, nor is there any appearance of a substantial miscarriage of justice," Justices Glazebrook, Arnold and France said.
