Artmedia Petrzalka captain Balazs Borbely has accused Celtic of treating their Champions League qualifier in Bratislava like a friendly.
Celtic crashed to their worst-ever European defeat in Gordon Strachan's first competitive game in charge.
"I think the Celtic players did not think Artmedia were much of a side," said Borbely.
"They seemed to treat the game more like a friendly. I could not believe how easy it was in the end."
Celtic now face one of their earliest European exits after the 5-0 hammering.
Not even a place in the Uefa Cup, of which they reached the final in 2003, is on offer for the losers in the second qualifying round.
"We knew that Celtic were a great side with great players, but after we scored the first two goals they opened up and let us in," said Borbely, who has said before the game that he was simply hoping to impress sufficiently to win a move to the Glasgow club.
"They had a couple of good chances, but they did not take them and we took ours. It's the biggest night in our club's history."
It was a demoralising night in the Tehelne Pole Stadium for the Celtic players and supporters and a sickening experience for Strachan on his big night in Bratislava.
Borbely is now backing his team-mates to add to their victory in the Tehelne Pole Stadium by scoring at Celtic Park in next week's second leg.
"We will go to Glasgow and we will know how desperate they will be and it still won't be easy," he added.
"We have never played in front of 60,000 fans before and it will be some experience.
"But I believe we can get a goal, which will leave them needing seven."