"I am leaving the Ukraine team. I took this decision in advance. I have chosen to focus on a club career because I am not young enough to combine both roles," the sport.ua website quoted him as saying after the 1-0 Group D loss.
The defeat eliminated co-hosts Ukraine from the tournament.
Earlier, the talismanic Shevchenko, who is 35, also announced he would retire from the national team after he plays in a friendly to say farewell to the fans.
Voronin, who turns 33 next month, has scored eight goals in 74 games for Ukraine. The stocky forward, who was Dynamo Moscow captain last season, has never played for a Ukrainian club.
He moved to Germany at the age of 16 to join Borussia Monchengladbach and played for several other German clubs also before an unsuccessful spell at Liverpool.
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