The Hungarian midfielder only moved to Russia in January 2012, but was open to the prospect of completing another switch 12 months on.
The chance to turn out in the Premier League appealed to him greatly, but Dinamo were unwilling to discuss a deal.
Dzsudzsak is disappointed to have seen one opportunity pass him by, but believes there will be more to come.
He told Nemzeti Sport: "I stay, but it wasn't up to me.
"Dinamo didn't let me go, not even to Liverpool. I can't say any more because it is not my position to do so.
"I want to say that in Hungary people have written me off, but it seems that some respectable teams still believe in me.
"I am not that disappointed. What I couldn't do during the winter transfer window can be done in the summer. It's also a nice feeling that in Moscow they have faith in me."