The hosts fell behind to a 28th-minute strike from Cristiano Ronaldo but kept battling right until the end and snatched an equaliser through Pontus Wernbloom with just under 30 seconds of injury time remaining.
CSKA now know that they have to score at least one in the return leg at the Santiago Bernabeu, but Slutsky is optimistic about his side's chances of springing a surprise in Spain.
"Two years ago we started with a 1-1 draw at home to Sevilla and were underdogs after the first leg as well," he pointed out to reporters after the game.
"Madrid still are the favourites but the outcome of this match gives us hope for a good result over the two legs."
Slutsky argued that while he side had struggled to secure a foothold in the game, Madrid had not created too many clear-cut goal-scoring opportunities.
"We made a poor mistake in the first half; otherwise it would have ended 0-0," he claimed. "We executed our defensive plan pretty well but failed to perform decently up front.
"The game was broken into separate episodes and one of them resulted in us scoring. We lacked a man in the centre of the park who would have directed our game.
"But we went all-in in the end and brought on some attacking players, increased the pressure on Madrid's defence and finally converted our last set-piece."
CSKA will travel to Madrid for the second leg on March 14.
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