"Our aim is to be in the final," Advocaat, who will quit his job to take charge of Dutch club PSV Eindhoven after Euro 2012, told a news conference in Moscow on Monday.
"I had recently signed a contract with PSV but right now I'm only thinking of my job with Russia.
"When people think of Euro favourites they usually name Germany, Netherlands and Spain. But don't count out Russia.
"If we play to our full potential, we could surprise a few people. I would call us a dark horse of the tournament. If you recall Euro 2004, nobody expected Greece [to win] it."
"I'm sad to say goodbye to Russia but I had no choice when the FA bosses said they would offer me a new deal only after the Euros," he said. "I just couldn't agree to such an offer. I'm not a young coach who hasn't achieved anything yet."
"I was disappointed with his recent form," he said of the former Everton midfielder, who joined Spartak Moscow in January.
"He didn't play very much at Everton, then didn't do well after joining Spartak. So I didn't think twice picking a left winger between him, Arshavin or [Alexander] Kokorin."
