The motivation worked as the Moldovan champions -- the first team in the country's history to feature in the Champions League group stage -- shocked the 13-time tournament champions 2-1 on Tuesday at the Madrid's Bernabeu stadium.
The upstart visitors went ahead after 25 minutes when forward Jasurbek Yakhshiboev put a free header past goalkeeper Thibaut Courtois. Karim Benzema equalised from the penalty spot after halftime before midfielder Sebastien Thill fired an 89th minute winner into the top corner.
"We believed we could win. I spoke to my teammates as captain, motivating them, saying 'why not dream?' This is football," Colombian forward Castaneda said. "Real Madrid are historic but on the pitch it's 11 vs. 11. We went for the win and got it."
The result leaves Sheriff top of group D with six points -- after winning both of their matches so far -- with Real Madrid in second.
"We played a really good game,'' said Thill, who became the first player from Luxembourg to score a goal in the Champions League. "The side were so brave with how we played and luckily enough I was able to score a bit of a stunner.''
Goalkeeper Georgios Athanasiadis, 28 -- who plays for Sheriff on loan from AEK Athens -- was named UEFA's Man of the Match for a display that saw him make ten saves.
"I'm really happy," he said. "It's very difficult to play against these teams, the best in the world. I'm emotional, if I carry on talking much longer, I'll end up crying."
For his side, Real Madrid manager Carlo Ancelotti blamed "little details" for the loss.
"More than worried we're sad," Ancelotti said in his post-match news conference. "The team played with a lot of intensity and commitment. I think the little details -- in the first half a cross, in the second half a throw-in -- decided the game. Often they don't cost you, but with bad luck, they do."
Ancelotti added: "We had a lot of opportunities. We could have been more precise in the last 30 metres but it's hard to explain this defeat with the game we played... It's a good lesson for the future. A throw-in, a cross, a corner, a pointless foul... They cost you. We lost and we didn't deserve it."
"We had so many shots, their goalkeeper made a lot of saves and I think you have to congratulate them for scoring two goals," said Real midfielder Casemiro. "We were in control of the game, had many chances and then they scored a wonder goal."
By contrast, Sheriff had three shots they had on target but were able to convert two that most mattered.
"I used to dream about winning at the Bernabeu," Sheriff's Peruvian defender Gustavo Dulanto said. "I've always followed Real, the club that's won the most Champions Leagues, and to have beaten them here at home is a great achievement."