Celtic manager Ronny Deila bemoaned "very, very poor defending" after watching his side surrender a lead in their 2-1 defeat by Aberdeen.
Leigh Griffiths' spot-kick put Celtic ahead but another penalty, converted by the Dons' Adam Rooney, levelled matters before Paul Quinn's late winner.
And Deila felt Celtic should have repelled the deep free-kick delivery from Niall McGinn which Quinn netted.
"We conceded a goal in an easy set play with a high ball," said Deila.
"The end of the game was very, very disappointing. They get one sent off and we should have attacked them and scored a second goal."
Aberdeen winger Jonny Hayes was shown a red card for a tackle on Mikael Lustig before the hosts went ahead, having levelled from the spot after Dedryck Boyata was penalised for his challenge on Graeme Shinnie.
"We played a controlled first half," said Deila. "I think we were the best team then, created the most chances but it was a tough first half as well.
"We get the penalty against us where I think it's no penalty. He's stands still and he doesn't take out his foot again. It was a very, very cheap penalty.
"I think we defended well in the first half today. We concede a goal at a set play and that's something we have to work on now. It's central, it's a high ball.
"[Goalkeeper] Craig [Gordon] could be out on that and also there are some players in the centre should never lose that header. Very, very poor defending."
Celtic were playing their first match since selling Virgil van Dijk to Southampton on the final day of the summer transfer window but Deila played down the impact of the Dutchman's departure from the back four.
"We work all the time on that," said the Norwegian. "That'll take, of course, a little bit of time but we conceded goals on set plays before Virgil went as well so this is an issue we have to really, really work with now."
Deila was also asked if he thought the foul on Griffiths by Andy Considine when the defender pulled the striker merited a red rather than a yellow card.
"It could be but in the end they get a man sent off and we didn't take advantage of that and that's very, very disappointing," he replied.
Last season, Scottish Premiership winners Celtic won all four meetings with nearest challengers Aberdeen and finished 17 points clear of Derek McInnes's side.
"They're a good team and they win games and if they continue to do that when we're going to have a serious challenger," Deila said of the Dons.
"We're disappointed today that we didn't perform better than we did but done is done now. We have to move on and learn from what we're doing."
Next up for Celtic is Ajax in their opening Europa League group match.
"It's a new game and new opportunities," added Deila.