Burnley's fine campaign so far has led to talk of the club potentially gunning for a European place, but Dyche wants to keep his feet on the ground because there are "a lot of challenges" still to come.
"It's a run of results and a start which the fans are enjoying and rightly so," Dyche told BBC Sport. "Football is about realities but also about dreams.
"It's a tough task for us winning games at this level but Leicester blew the roof off dreams in football - there's no bold statement from me on that. Tonight was a different style of getting a result. It was an ugly game at times in harsh conditions.
"We found a way to win and a real fine goal. Sometimes that's football. We're not the real deal, we're a side that are improving. We've got an aligned thinking here, there's no superstars, no favourites from me. I believe in all of them. We've got a group of people - there's a belief in everything we do here.
"I keep reality because this division will eat you alive. We're having a real go at what we can achieve this season. I'm not being negative. I'm a realist, there's a lot of challenges coming our way. The fans and the town have got to enjoy these times, why wouldn't you?"
Since 2003, the only club to have qualified for the Champions League other than those in the top six after last weekend was Leicester City in 2016.