Tottenham are second only to Arsenal in the Premier League after collecting 13 points from their opening six matches.
Chelsea, who began the season as favourites for the league, looked very much the inferior team during a one-sided first half at White Hart Lane on Saturday, but Tottenham failed to take their chances and ended up settling for a 1-1 draw following John Terry's equaliser.
Still, the early signs of the post-Gareth Bale era are encouraging for the north London club as the likes of Roberto Soldado, Christian Eriksen and Paulinho adapt to their new surroundings.
Such performances have led to suggestions that Spurs have a squad capable of winning their first league championship since 1961, but Holtby insists Tottenham's sights are firmly set on a top-four finish.
"Everyone can dream but our main aim is to get Champions League football," the Tottenham midfielder said.
"I think we've got the quality and the ability in the whole squad to do that, I'm very confident.
"It's a long season and everyone has to be at the top level to reach that."
Eriksen, Andros Townsend and Paulinho all impressed during a fast-paced first half in north London, but it was the introduction of the Tottenham target that got away - Juan Mata - that put Chelsea back in the game.
Tottenham, encouraged by Mata's surprising lack of first-team action this season, made an enquiry for the Spaniard in the last few days of the transfer window, only to be told that he was not for sale.
The fact that another Spurs target Willian was not even on the Blues' bench shows how much of a star-studded squad Jose Mourinho has available to him.
Andre Villas-Boas was looking to get one over on his old mentor, but Holtby still thinks his manager can be proud of his team's efforts.
"This was a big test, absolutely, and I think we're in a good way and playing a wonderful season," the German said.
"I think the manager was proud of us and how we committed to the game and how we fight in our game week in and week out. We've had a lot of games now in the last couple of weeks so everyone's just done a fantastic job.
"We have to keep on progressing. It's very early in the season, we have to keep working hard. We've got a couple of games now where we have to get some points and stick up top and defend our place up in the top four."
Holtby endured a difficult start to his Spurs career after his move from Schalke in January, but he soon improved and by the end of last season he had started showing glimpses of real quality in his favoured number 10 role.
Townsend's return from QPR, and the signing of no fewer than five midfielders to the Spurs squad mean Holtby's chances of first-team football took a hit, but the 23-year-old is loving life at White Hart Lane.
"I didn't do the best that I can do last season, but I've progressed and now I think I'm getting more involved," said Holtby, who set up three of Tottenham's Capital One Cup goals against Aston Villa in midweek.
"I feel very comfortable and very proud to be here at this club, and I just try to do the things that I do best.
"Roberto Soldado is a fantastic striker. I hope one day I can play behind him and I'm learning Jermain Defoe's runs too.
"It's easy for a number 10 or a central midfielder to put these players in because they make some wonderful movements, and I'm just happy to be here."