A solitary Ashley Barnes strike five minutes into the second half was enough to give the top flight's bottom side their first win of the season at Turf Moor, in a game that saw Hull finish with 10 men after Curtis Davies was forced off with a back injury with the visitors having already used all of their substitutes.
After seeing his side go 10 league matches without a victory, Dyche acknowledged he had been fearful of seeing another opportunity go begging.
The 43-year-old was therefore delighted to see Burnley end their barren run, and says everyone at the club now knows what is required for the remainder of the season.
"[In the] first half I thought we were excellent," said Dyche. "I thought we had enough chances to be one or maybe two to the good, defensively we were good and it has been a few times this season.
"But you go in at half time and you think 'is this going to be one of those games again?'
"I mentioned it to the lads that this is not a situation where it's 'good old Burnley' again.
"We know that alright and doing well is not good enough - you need to do even better, so I was pleased with the way they came out second half.
"We got the goal and it was a bit nervy after that, which you expect. Even when they're at 10 men you think 'do you keep it or play it forward?'
"The decision-making went a bit soft by our standards but the marker's laid down, you get your first win and everyone feels better about themselves."