Charlton Athletic 2 Manchester City 2
The Addicks grabbed a stoppage-time equaliser that just about keeps alive their hopes of securing European football for the first time.
After the draw Curbishley said: "Our performance in the first half was abysmal and really shocked me.
"I'm lost for words. We made Manchester City look like Brazil and nobody on the field tried to sort it out. We should have been three or four down at half-time.
"We needed gallons of desire in the second half and the only form of comfort I can take from the game is that we kept going and managed to get that late goal.
"But I'll have to take a serious look at how we played in the first half. It was a complete shambles and we need more desire."
City must be wondering how they failed to win the game after dominating for long periods but manager Stuart Pearce, in his second game in charge, was delighted with the way his team played although frustrated at their failure to take the three points.
"I thought we were exceptional at times today and had enough chances to win comfortably," he said.
"But I don't give anybody sympathy and I don't ask for it. I'm only disappointed for the players and I'm upset for them because they deserved to win."
Pearce, who has so far only been appointed as Kevin Keegan's replacement until the end of the season, said there was a nice bond of togetherness amongst the players.
"I want the job on a full-time basis and so far the board has been very positive but I know that this is a results game," he added.
City took the lead after just four minutes when Robbie Fowler's corner was headed goalwards by Richard Dunne and the ball was deflected into the net off Charlton defender Hermann Hreidarsson.
Dunne however will claim what would only be his second goal of his City career and his first in three-and-a-half years.
Jonathan Macken, who has scored only once in 23 games for City, squandered two gilt-edged chances before Charlton levelled when David James failed to hold a cross from Jerome Thomas and Shaun Bartlett bundled the ball over the line.
City, who continued to dominate the game, regained the lead six minutes before the break when the influential Fowler scored a poacher's goal from Joey Barton's corner.
Curbishley responded to his team's inept performance by replacing Mark Fish and Jonatan Johansson with Jonathan Fortune and Francis Jeffers and reverted to a 4-4-2 system.
His team showed a marked improvement and they were unlucky not to equalise when skipper Matt Holland, who was making his 500th career appearance, rattled the crossbar with a header.
But Charlton got their undeserved equaliser when Luke Young's cross was headed across goal by Jeffers and Chris Perry fired in from close range at the far post to score his first goal of the season.
MAN OF THE MATCH: Robbie Fowler (Manchester City) - Scored City's second goal and was influential in everything the visitors did. He looked to be back to his best form as City were unluckily denied three points at the death.