Captain Ryan Shawcross insists Stoke's players still believe in manager Mark Hughes.
The Welshman is under pressure with the Potters having made their worst start to a Premier League season, taking only 16 points from 17 games.
Hughes has been manager of Stoke since May 2013 and oversaw three successive ninth-placed finishes, the club's best since the 1970s, in his first three seasons.
But last term they flirted with trouble before finishing 13th and they have conceded 36 goals so far this campaign, more than any other team.
Supporter unrest has been growing and loud boos and chants of 'you don't know what you're doing' could be heard when Hughes substituted Xherdan Shaqiri late on in Tuesday's 1-0 loss to Burnley.
Shawcross said: "That's the game we're in and the manager knows it. He knows we need results. If we stick together as we have done over the years then it helps a lot.
"We know he's a quality manager, we believe in him. Unfortunately we are going through a bad period at the moment but, as we've shown over the five years he's been here, I think he's been one of the most successful managers we've ever had as a club."
Although Tuesday's result was disappointing, the performance was at least a great improvement on last weekend's 5-1 defeat by Tottenham, after which the Stoke squad were confronted by angry fans at the railway station.
"Obviously we got a bit of stick after the Spurs game, which was fully deserved," said Shawcross.
"I thought we put on a half-decent performance in response to that and we were unlucky not to come away with a point at least. We're really disappointed.
"It's the way it's going at the moment. Unlike at Spurs, I thought we worked really hard and unfortunately it was just that little bit of quality didn't get us a goal and then in the last minute they pinched the winner.
"We had dealt well with them all night, I don't think Jack (Butland) had a real shot to save, but at the moment it's not going for us. It will change.
"The lads are all gutted, the management team are all gutted. We just have to move on to the next game now and make sure we pick up a win."
Defender Geoff Cameron joined Shawcross in backing Hughes, who now faces a potentially make-or-break game against fellow strugglers West Ham at the bet365 Stadium on Saturday.
"If we can have that same effort, same desire, same work ethic in every game for the rest of the season we'll be fine," said Cameron.
"People have been saying 'Hughes out', we know, but no; when you see what he has done for the club, he's a great manager."
Cameron's return to the starting line-up after more than six weeks out following the concussion he suffered in training was a major positive for Stoke to take away from Turf Moor.
The American was unable to train for more than a month and revealed he is still dealing with the after-effects.
He said: "I'm all right. I get headaches here and there but it's good to get back on the pitch."