The result saw Spurs book their place in the knockout stages of Europe's premier club competition for the first time since 2011, with England international Alli proving to be the star of the show as he netted a goal in either half.
Mauricio Pochettino's side have now taken four points off Real during this season's group stage and Alli insists he was not surprised by the manner of their latest victory, particularly after their impressive display in the Bernabeu a couple of weeks ago.
"To be honest, no," Alli told BT Sport when asked if he was surprised by Tottenham's performance.
"We spoke after the game at their place and said we couldn't believe how much space we had at times and that the easy pass looked too obvious at times and we were too sloppy.
"I think we knew that if we were solid at the back we'd get the chances and with the team we've got here we don't just want to be competing with these teams, we want to be winning."
Alli was understandably delighted with the result and his own contribution, but he conceded the scoreline could have been even better for Spurs had they been more clinical in front on goal.
He added: "It was a fantastic performance from us. We stuck to the game plan and made a lot of chances - it could have been more but we're very happy with the result."