The newly promoted side picked up their first point of the campaign on Saturday, courtesy of a 0-0 draw with Manchester United at Turf Moor.
Burnley have faced a tricky start to the season on their return to the top flight, with games against Chelsea and Swansea City preceding the home game against Louis van Gaal's men.
Yet Dyche expects Burnley's supporters to remain level-headed and not become too despondent should points prove hard to come by.
"I think they know the script. They're used to it up here; they've had a few knocks in their time," said Dyche.
"They know we're underdogs in virtually every game, if not every game we play. I think they're aware [of that], they're reality-bound and certainly since I've been here I've always been honest with them.
"They probably saw the fixtures and thought that's a tough three games [to start the season]. They all are, but particularly the first three that came out the pot."
Dyche is confident his team can do their fans proud, regardless of whether they are successful in retaining their Premier League status.
"The thing I'm sure of, whatever happens to us this season, they [the fans] have got a group of players they know will be relentless and give everything to win football matches," he added.
"I'm convinced they know that and that is what I promised I would give them when I got here."
