Danny Rose says Tottenham were motivated by silencing Arsenal in last night’s EFL Cup quarter-final after the Gunners “celebrated like they won the league” following their 4-2 victory earlier this month.

The England left-back said Arsenal “got ahead of themselves” after winning the first north London derby of the season, on December 2, and described Tottenham’s 2-0 win at Emirates Stadium as “karma”.

Pierre-Emerick Aubameyang shared a video of the Arsenal dressing room after the game and an Instagram post from Aaron Ramsey appeared to mock Eric Dier, who sparked a first-half brawl when he celebrated his equaliser. Sead Kolasinac was among the other Arsenal stars to overtly celebrate via social media, while the club’s Twitter account this week showed Aubameyang and Alexandre Lacazette – both of whom scored in the win — taking part in a commentary of the game’s highlights.

Arsenal have since lost their 22-game unbeaten run and fallen back behind Spurs in the league and Rose challenged their rivals to see who would finish higher at the end of the season.

“We were fully relishing the opportunity,” Rose told Standard Sport after goals from Heung-min Son and Dele Alli set up a League Cup semi-final against Chelsea, who beat Bournemouth 1-0.

“Our only motivation was remembering the nonsense that Arsenal posted after the game a few weeks ago. That was our motivation. Players that have only played 10 games for Arsenal were getting ahead of themselves. We used that in a positive way. It’s karma. They fully deserve what they got.

“We had the motivation of getting to the semi-final, so we’re over the moon. But the cherry on top was silencing them after remembering how they celebrated like they had won the league. We’ve put that result right. We’ll see where they are come the end of the season and we’ll see where we are.”

Rose skippered Spurs for the first time since January 2016 on his third straight start since returning from a groin problem and showed signs of the form that made him one of the best left-backs in Europe before a serious knee injury in early 2017. In the past two years, Rose struggled with further injury problems and depression and he came close to leaving Spurs in the summer. But he revealed conversations with manager Mauricio Pochettino had persuaded him to stay at the club.

“[Captaining the side again] was a very proud moment, especially because we won,” he said. “If I look back at where I was a year ago, I wasn’t playing too often. Now I have played three games in a week, we drew with Barcelona and won a difficult game against Burnley. And we won another difficult game last night, which was very special.

“After the World Cup, I called the manager and we spoke. We spoke for an hour before the first game at Newcastle and we spoke for an hour after that. The one main thing that stuck out from what he said to me was: ‘Danny — stop wasting time’. So yeah, I’m not wasting any more time. I’ve got my head down again and I’m doing okay at the minute. I’m trying to get back to where I was a couple of years ago.

“He meant, ‘Be fully focused’. On the pitch. And if you’re not fully focused then you’re free to leave the club. So I told him that I am fully focused. And I’m going to be here to fight and help the club progress. And I hope that I am showing that in my performances and in training as well.”

Spurs now face a two-legged semi-final against Chelsea as they bid to end an 11-year trophy drought. “It’s going to be a hard two games but we are all excited,” said Rose. “Winning any trophy would be special.”