It was a positive response from Spurs after losing at fellow title rivals Manchester United in late October, and midfield marshal Dier believes Mauricio Pochettino’s side are on the right track.
“I believe what we are doing is right, that has been the case for a long time,” he said.
“Win, lose, or draw against Real Madrid, that would have been the same. Winning that game has obviously given us confidence as individuals and as a group.
“You’ve got to keep trying to improve and push the boundaries. That’s the same for club and country; you’ve got to keep trying to improve. That’s the key.”
The contrast between the dazzling performance against European champions Madrid and the gritty nature of the struggle against Palace has also Dier confidence that Spurs will be in the thick of the title race come season’s end.
“The games we have had in the last month have been really good and the results have been very positive,” he said.
“Obviously, Manchester City have been fantastic recently but there is so much football to be played before the end. I’m sure there are going to be a lot of twists and turns before the end.”
Dier was one of six Tottenham players called up for England duty, but that number has been cut to three after Harry Kane, Dele Alli and Harry Winks withdrew from the squad due to injury.
Despite the mixed reputation attached to international friendlies in recent times, Dier says it is still an honour to step onto the pitch for England.
“Playing for your country is the pinnacle of football,” he said.
“It is what you all want to do and it has to be special. I think that it’s essential, you cannot just think you will be in every squad because you have done ‘X and X’ in preview years, it has to be constant.”
Dier believes the mood among the England squad is more competitive than ever – a belief backed by the fact that Three Lions mainstay Alex Oxlade-Chamberlain was dropped after a series indifferent performances for Liverpool.
He said: “You always have to be on your toes to get the call-up otherwise you can become complacent and I don’t think that is a good thing.”