Cardiff, who had to play most of the second half with 10 men after Joe Ralls was sent off in the 58th minute, remain without a win this season and fall to bottom of the table.
Spurs have 18 points after eight games – their joint-best total – and are third in the table, one point behind leaders Manchester City, who are ahead of Liverpool on goal difference.
Their next match is against West Ham on 20 October after the international break, their first of seven games in 22 days.
“We are one point off the top of the Premier League but we need to improve a lot,” Pochettino said.
“Now we have two weeks before the next game – but it is a very tough schedule when we return.”
Spurs produced a lethargic performance against a battling Cardiff, who could have equalised midway through the first half but Toby Alderweireld cleared Josh Murphy’s effort off the line.
The hosts lost their way after going in front but improved at the end of the first half, with Lucas Moura missing two good chances and Son Heung-min also shooting over.
Immediately after half-time, Cardiff captain Sean Morrison brilliantly blocked Moura’s shot on the line after Harry Kane’s initial header had been saved.
Ralls was then sent off for a cynical challenge on Moura but minutes later Morrison had a header turned onto the post by Spurs goalkeeper Hugo Lloris.
It seems remarkable that Spurs were described as a club in “mini-crisis” last month after losing three consecutive games – because now they have achieved their joint-best start to a season.
That tricky period at the start of September included league defeats by Liverpool and Watford as well as a Champions League defeat to Inter Milan.
The three points against Cardiff were secured despite a ponderous display which came three days after Spurs were beaten in an enthralling encounter in the Champions League by Barcelona.
Pochettino made just three changes to his team, although he had little other option with key first-team players Dele Alli, Christian Eriksen and Jan Vertonghen all injured.
Spurs’ build-up play was slow and the movement up front was not as evident as in previous games.
When they did create chances they were wasteful. Moura headed off target in the first half and put a shot from seven yards wide, although in the second half he could have done little more with his shot that was brilliantly blocked by Morrison.
Captain Harry Kane was quiet. His two shots on target were a shot from distance in the first half and a header at the start of the second.
