Hart gifted possession to the hosts before Andre Silva netted the first of two second-half goals following Jota’s equaliser.
The former Manchester City player told BT Sport: “I’m at fault for the second goal, no doubt about it, but that’s the way the manager wants us to play so that’s the way we play.
“Sometimes it’s going to hurt us but ultimately most of the time, as we proved tonight, we got through the press and gave ourselves real good opportunities to score goals.
“They were pressing with three and I wasn’t quite sure whether to go to the centre-half or Greg (Taylor) and I decided to go to Greg and I missed. They are the simple facts but it’s high-level football and something that I love playing. You make a mistake and you are going to get punished.”
Postecoglou is concerned about an injury that forced skipper Callum McGregor off in the first half.
The midfielder appeared to get injured as he lost possession following a short corner immediately before Leipzig countered for Christopher Nkunku to score the opener.
“It doesn’t look good,” the Celtic manager told BT Sport. “We were a bit unlucky with the goal because he went to have a shot and something tweaked in his knee. He put in an enormous effort to chase back and it was his toe-poke that put the guy through.
“It doesn’t look good but I’ll wait to see what the doctors say.”