Rooney is set to miss the three group games at next summer's tournament but the FA have appealed in an attempt to get the ban reduced.
Dzodovic said he felt the punishment was harsh and appeared keen to help Rooney's cause when it was revealed last month that he would contact UEFA.
But the Spartak Nalchik stopper insists his part in the process has been exaggerated by a Russian paper.
"'The source of all this is one of the newspapers in Russia, which published that I wrote some kind of letter to UEFA but this can't be further away from truth," he told Montenegrin newspaper Vijesti.
"That newspaper started an initiative, there were some Manchester United fans involved in all this. The editor asked me, if I want to support them and I said yes, why not, but it is a lie that I wrote a letter of support to UEFA."