The Premier League leaders saw their lead at the top of the table cut to seven points after the setback at their Stamford Bridge home.
It looked like business as usual for Conte’s manne at the start when Cesc Fabregas tapped in from close range to give them the lead after just five minutes.
But a quick response from Wilfried Zaha with a low drive and a Christian Benteke chip-kick saw the Eagles ahead after 11 minutes as Sam Allardyce’s team took the points.
Afterwards Conte said: “I think today we deserved at least a draw.
“I don’t want to say a win, but at least a draw. We created many chances to score, we dominated the game against a very strong team with really good players.
“It’s a pity but it wasn’t our day. For you [the media] it’s a good result because it makes the championship more interesting.”
The result ends a run of eight games without defeat for the Blues and Conte is now focused on Wednesday’s match with Man City.
The Italian coach adds: “We all know the strength of their team, but for now the most important thing is to rest and recover well.”