The Russians have been written off by many pundits ahead of their meeting with Los Blancos at the Santiago Bernabeu on Wednesday night, despite the fact that they held Jose Mourinho's star-studded lineup to a 1-1 draw in their first-leg meeting at the Luzhniki Stadium.
However, Dzagoev insists that Leonid Slutsky's troops are paying little heed to the naysayers.
"Madrid may be the favourites, but those who say we have no chance are very wrong," the 21-year-old midfielder told Uefa.com.
"There is nothing impossible about this task. None of us are going to just roll over – we actually have victory on our minds.
"There is no mental pressure on us: Madrid are world-class opponents, so the onus is on them."
Dzagoev was unwilling to go so far as to call the meeting with Madrid the biggest game in CSKA's history, but he did admit that dumping the runaway La Liga leaders out of Europe's elite competition would represent a significant achievement for the club.
"Every fixture is important in its own way," the Russia international mused. "We can make history with a positive result at the Bernabeu.
"Madrid have a lot of stars: Cristiano Ronaldo, Kaka, Mesut Ozil, Karim Benzema and Xabi Alonso. Beating them would give us a lot of positive emotion and momentum."
CSKA's clash with Madrid in the Spanish capital gets underway at 20:45CET on Wednesday.
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