The 26-year-old midfielder was a reported target for the Premier League giants, just 12 months after he signed for the Russian side from rivals Anzhi Makhachkala.
Reds boss Brendan Rodgers had been looking to strengthen his Anfield squad, and completed deals for Daniel Sturridge from Chelsea and Philippe Coutinho from Inter Milan.
However, the Northern Irishman's attempts to bring Dzsudzsak to Merseyside were in vain, after the Hungarian international was denied the opportunity to even speak with Liverpool, by his current club Dinamo Moscow.
"I want to say that in Hungary people have written me off, but it seems that some respectable teams still believe in me."
Dzsudzsak admitted that the chance to turn out in the Premier League appealed to him greatly, but said that he wasn't too disappointed to see a potential move break down, because he is confident that if he maintains his form, then more opportunities will follow in the future.
"I am not that disappointed," he added. "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."