Last term's Championship runners-up ended a 10-game winless run in the top flight on Saturday, beating Hull City 1-0 to move to within two points of safety.
But Dyche is aware further victories will be required if Burnley are to climb out of the bottom three.
"At the end of the day it's not about just one win," he said. "It's great and I'll enjoy it, don't get me wrong, but what I'm suggesting is that it's more than one win needed, we know that.
"But it is important to get that first win of course, psychologically for the players, improving belief in the players, belief in the town and belief we can at least compete and give everything in this division to try and make the impossible - which is what everyone else is telling me by the way - possible."
The 43-year-old was relieved that his players finally got the win that he felt their performances had merited, and hailed their response to the result.
"They didn't go overboard about it," he added. "Our internal view is different to the outside view. We've been frustrated by games, we've felt we've deserved wins already and haven't got them.
"But they're very pleased that their work has come with a reward, which is the first win.
"We're a work in progress. A lot of the players haven't played at this level and this is a completely different level to the Championship."
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