RECAP: Burnley 1 Spurs 0
and live on Freeview channel 276
That victory came just hours before Spurs left it late to edge a five-goal thriller over champions Manchester City at the Etihad.
However, despite putting three past the leaders on the way to securing three points, the former Italy national boss is wary ahead of Wednesday night's game at Turf Moor.
He said: "Maybe it's the worst period to play against them because in the last period they have had fantastic results and played a good game," he said.
"They drew with Manchester United, and away at Arsenal, and they beat Brighton 3-0.
"They lost only 1-0 against Liverpool but the game was in the balance. For sure, for us they will be a really tough team, we have to know this."
Sean Dyche's side beat tonight's visitors 2-1 exactly three years ago when Chris Wood and Ashley Barnes scored either side of Harry Kane's equaliser for the away side.
"It's never easy to play against Burnley and they have a good manager that is showing in these years that his managing is very, very good and maybe he could deserve something more," continued Conte.
The two managers have met four times previously when Conte was at the helm at Stamford Bridge with Chelsea.
The ex-Juventus manager has taken seven points from their head-to-heads, but suffered defeat in the defence of their title at the start of the 2017-18 campaign when Sam Vokes (2) and Stephen Ward were on the scoresheet.
"I appreciate his job and what he's doing with Burnley," said Conte. "Remember one month ago many people said Burnley were relegated, but I'm sure they can save this season and I think Burnley are doing a fantastic job."
LIVE: Burnley 1 Spurs 0
Full-time: Burnley 1 Spurs 0
Ben Mee’s finish makes it back-to-back wins for Burnley.
Weghorst leaves the field to a standing ovation and Ashley Barnes is his replacement.
Burnley can’t clear their lines and Bergwijn’s side-footed attempt is saved by Pope.
Roberts rolls the ball into Brownhill and the midfielder’s attempt from 20 yards out dips just wide of the post.
Over the top
The ball falls nicely for Moura inside the box but he skies his effort.
Mee gets two bites of the cherry from McNeil’s corner and Rodriguez somehow pokes the ball over the bar from close range from his captain’s second attempt.
Bergwijn replaces Sessegnon for Spurs.
GOAL: Burnley 1 Spurs 0
Mee heads Brownhill’s free kick back across goal and the skipper finds the corner.
A whisker away
Spurs break through Son, who off lays the ball to Kulusevski. He uses Pieters to shield his shot, which slides just wide of the post.
McNeil gets the ball out of his feet, whips in a wonderful cross and Rodriguez’s header forces the save from Lloris.