Brendan Rodgers admits he is facing the biggest test of his Celtic tenure after their 2-1 defeat at Kilmarnock confirmed the Hoops' worst start to a Ladbrokes Premiership season in 20 years.

Defender Stuart Findlay's dramatic injury-time header from a Chris Burke corner gave Killie a stunning victory, after Burke's drive had cancelled out Leigh Griffiths' first-half opener.

The Northern Irishman has enjoyed nothing but domestic success since arriving at the Parkhead club in 2016 and his side finished last season as unprecedented double treble winners.

However, after six games the champions have only 10 points and are six points behind leaders Hearts, their poorest start since the 1998-99 campaign under Jozef Venglos.

Asked if faced the biggest challenge of his time as Celtic boss, Rodgers, who will have defender Filip Benkovic's Achilles problem assessed after he pulled up in the warm-up, said: "It is. It's a challenge.

"We have to accept that. There's no doubt we need to be better. When you're at the biggest clubs and you don't win the heat comes on to you.

"That's when you show you're a Celtic player, manager, member of staff.

"You come together. When you lose games the spotlight will always be on you.

"You have to work hard, do the basics right. The basics cost us this time.

"It hasn't been great, but we have to accept that. We're the only ones who can make it better and get more consistent results."

Celtic have lost to Hearts and Kilmarnock and have drawn with St Mirren in the league.

Rodgers believes opponents are getting better, while also having a "new-found respect" for his side.

The former Liverpool and Swansea City boss said: "The teams are playing deep. At St Mirren we saw it, even when we had 10 men. You saw Rangers come and sit deep, Kilmarnock did that too.

"It's up to us, we have to find the answers to that. That's the job.

"We have to analyse the game and build the mentality again to win your next game.

"I'd have been disappointed to draw, but to lose is bitterly disappointing. It was a scrappy sort of game, but I still feel we had the better moments and more control."

Kilmarnock have now gone four games without defeat to Celtic and manager Steve Clarke praised former Parkhead youth player Findlay for playing through the pain barrier.

He said: "I was pleased for Stuart Findlay. He didn't train all week, but he put his body on the line.

"He was struggling at half-time but those are some of the rewards the footballing Gods give you.

"Stuart had a bang on the knee and it was sore through the week. He got another bang in the first half but we've got good character in the squad.

"We were competitive. I was a little bit disappointed to be down at half-time because I didn't think we deserved to be after we started really well.

"We had decent control. Two mistakes on ball into box cost us, but we reacted well.

"We spoke at half-time about believing. We've shown we can compete with the big teams. Second half we competed well and deserved to get back in."