Sean Dyche believes Burnley fans will stay firmly behind their team because they understand the size of the task facing the Clarets.
The Championship runners-up began the season as favourites for relegation and after nine games are still looking for their first Premier League victory.
Their latest reverse came at Turf Moor on Sunday as Everton clinched a 3-1 victory, but the players walked off the pitch to applause from the home supporters.
Boss Dyche said: "I thought the fans were terrific. I think they get the challenge. With all this coverage now, every fan out there can see it right in front of their face.
"Our club get promoted, and they don't come in thinking, 'Oh well, that's it, we'll just roll up the table'. They look at all the signings, all the teams they're playing against, the quality, the worldwide class that's out there.
"The fans are backing the players and I've told them that's important. I think they've been absolutely fantastic and we will still need them.
"They wanted it, we wanted it, the town wanted it, it's here, it's real. That didn't mean it was going to be an easy ride."
Burnley were behind inside four minutes through Samuel Eto'o's header, but Danny Ings levelled things after 20 minutes.
Romelu Lukaku, whose mistake led to Burnley's goal, put Everton back in front nine minutes later and Eto'o wrapped things up five minutes from time.
The main positive for Burnley was a first Premier League goal for last season's top scorer Ings, who became the first Clarets striker to find the net this season.
"It was a very good finish," said Dyche. "He looked nice and sharp and he's growing again.
"He had a soft start to his season in the Premier League and then getting the injury. Weirdly I thought that might do him good, and he looks nice and lively.
"All the strikers need goals. They're all in there, they're all clambering. We have to keep believing it will come."
Everton won for the first time in the Premier League after a Europa League game and made it back-to-back league victories.
Manager Roberto Martinez said: "Coming here today I knew it was going to be a really tough game.
"Burnley have been very unfortunate this season that they haven't got more points or wins, because I think their efforts deserve more.
"I knew they would play with energy, pressing us high up and stopping us from playing and I thought we were very professional.
"We controlled the game well, we defended extremely well apart from the goal that we gave away, then going forward we picked the right moments, and I thought that was a really good sign.
"I thought the performance was perfect to set our season up."
Source: PA
