LONDON – At the final whistle, relief could be felt in the stands as Tottenham fans jumped out of their seats, head coach Ange Postecoglou calmly walked onto the pitch and the song “Glory, Glory Tottenham Hotspur” blared from the stadium's speakers.

This song may not seem appropriate these days. No one needs reminding here that it has been almost 17 years since Spurs last won a trophy. However, in Postecoglou's second season at the helm, the clear aim is to end this winning streak.

Wednesday night's narrow 2-1 win over Manchester City takes them into the quarter-finals of the Carabao Cup and is one step closer to that goal. However, their performance may raise questions about whether this team can achieve this.

“I thought we defended well because we really didn’t miss too many clear chances,” Postecoglou said.

“We had some really good chances to finish the game but we didn't take them, but the boys showed great resilience to open the game.”

There are clearly positive aspects to be taken from the game. Beating City – a team Postecoglou describes as the “gold standard” – is never something to sneeze at. They are the first team to do so this season, the first since Manchester United in the FA Cup final last season.

“They (the city) can ask any question there is and by and large I thought we had it,” Postecoglou said. He too will be grinning as his team display a refreshing pragmatism and the two defensive midfielders largely keep City at bay.

So perhaps it's difficult to water down a Tottenham win – “ultimately,” Postecoglou said, “the most important thing you have to do is win” – but it begs the question of whether they are ready to end the trophy drought remain.

This game was theirs. City fielded a weakened starting XI and it took just five minutes for Timo Werner to score his first goal of the season after Dejan Kulusevski beat him at the back post with a low cross to the opposite side of the penalty area. Pape Matar Sarr followed up 20 minutes later, firing the ball from outside the penalty area into the bottom right corner with a great, curling shot.

But despite a two-goal lead in the first half, Spurs failed to capitalize and never looked confident. The missed opportunities kept piling up. In the first half, Werner received the ball from an errant and sloppy pass from İlkay Gündoğan in City's 18-yard penalty area. The German striker should have scored, but he only found goalkeeper Stefan Ortega's gloves. When City reduced the deficit to just one goal when Matheus Nunes hit the post just before half-time, Spurs' task turned into one of consolidation.

The second half brought more failed attempts. Just a few minutes after the restart, Werner missed a one-on-one before Kulusevski did the same on the other side. Later, substitute Richarlison had the edge and was given a one-on-one throw-in thanks to a mistaken throw-in from City, which Spurs again failed to convert.

After Savinho was substituted through injury, City almost equalized through teenager Nico O'Reilly, but Yves Bissouma made a heroic save off the line.

Spurs have been criticized this season for failing to finish games, most recently blowing a two-goal first-half lead at Brighton & Hove Albion. Domestically, this is their first win this season by a single goal – this time they took a hit and stood. In this light, Postecoglou's lack of ruthlessness, while still showing determination, may not be a cause for concern.

The Australian was adamant he can turn the tide at Spurs by removing the 'Spursy' label and hoping he can continue his winning ways in his second season as a club manager.

“It’s about continually pushing this group to become the team we want to be,” he added.

“We're not there yet, that's fair to say. As I said yesterday, I'm really optimistic about this group of players. They have a really high ceiling and we just have to keep focusing on that.”

Spurs fans will be praying that Postecoglou is right. After the final whistle, they sang with relief. “Glory, Glory Tottenham Hotspur” continued over the speakers, followed by Gala’s “Freed from Desire”. The Spurs fans were thrilled.

An hour later, however, another sobering message came. Tottenham faced Manchester United at home in the quarter-finals. It means another difficult draw as they look to lift their first trophy since 2008 and shorten the feeling of relief.