Celtic fans should be "alarmed" by the side's worst start to a league season for 20 years, says Brendan Rodgers.

The champions surrendered a lead before slumping to a 2-1 Scottish Premiership defeat at Kilmarnock on Sunday.

After back-to-back domestic trebles, Rodgers' team have only 10 points from six league games and are in sixth place, six points off leaders Hearts.

"When you are a huge club, the demand is to win," the Celtic manager told BBC Scotland.

"In the last couple of years we've done that really well and playing in a style that is synonymous with the club. It hasn't been the same but we have to work to make it better.

"It's a poor result for us but we have to go away now and take our medicine and get ready for Wednesday [a Scottish League Cup quarter-final trip to St Johnstone]."

When asked if Celtic fans should be alarmed, Rodgers replied: "Yes I think they should."

Leigh Griffiths nodded Celtic ahead after a poor attempted clearance from Killie's Greg Taylor and held that lead until half-time.

But following a corner, Chris Burke lashed home an equaliser and Stuart Findlay's stoppage-time header snatched victory for the home side.

Rodgers said his team "had fairly good control of the game" but "didn't do the basics well".

"From the first corner we didn't come out well enough and protect the space. Burke gets in on the right side," the Northern Irishman added.

"Then the second goal is just basic. It's a corner. You can see Kilmarnock didn't even want to take it. Burke puts it in and we don't defend it strong enough.

"To lose the game is disappointing. We just have to continue to work. There are probably a number of reasons for it but we have to stick together.

"You can only ever do your best; that's what we always say to the players. But we can be much better."

Rodgers 'didn't have a lot of answers' - Analysis

Former Celtic goalkeeper Pat Bonner on BBC Scotland:

"It is a strange statement from Brendan, really strange. When things are not going well, the manager has to keep the environment right, and keep the confidence up, not just of the players but the fans also.

"So it is a strange statement for me. He looks very down. When he was asked why, he didn't have a lot of answers to it. I don't know if he really sees why."