England midfielder Alli scored twice, either side of half-time, and Christian Eriksen was also on target at a jubilant Wembley on Wednesday as Spurs claimed a famous win over the 12-time European champions.
It took Spurs into the last 16 with two games to spare and left Mauricio Pochettino's side three points clear of Madrid at the Group H summit.
"It was a fantastic display by us," Alli told BT Sport.
"We knew if we stuck to our game plan and were solid at the back then we'd get chances. We're very happy with the result.
"We don't want to just compete with these teams -- we want to beat them. I'm happy to get two goals, but more importantly it was a win."
Spurs manager Pochettino echoed Alli's words and said the result would bolster the self-belief within his squad.
"I'm very proud of my players and I congratulate them. I'm so pleased for Dele and our fans," said the former Argentina defender.
"The victory is so important for us and the players. It's a win over Real so it's great for the club and fans.
"There's a long way to go until the end of the season. What's important is trying to achieve our challenge and target.
"Of course this win gives us great belief for everyone and confidence. We are now in the next stage of the Champions League."
It was another chastening result for Madrid hot on the heels of their shock defeat at Girona last weekend.
The Spanish giants are eight points behind La Liga leaders Barcelona and are yet to book their place in the Champions League last 16 with two group games left.
Asked if Madrid were in crisis, boss Zinedine Zidane said: "No. I don't think we're lost.
"Maybe we are missing the calm we normally have in front of goal.
"We are making chances and not taking them but for sure we will turn this situation around.
"When you lose two games in a row, your confidence can't be great but we have three or four days to rest and think about the next game."
AFP
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