Ezequiel Lavezzi opened the scoring for Laurent Blanc's hosts on four minutes with a sweetly-struck half-volley, but Eden Hazard kept his cool from the penalty spot on 27 to draw Jose Mourinho's men level.
Hazard hit the upright in a lively first half for the Belgian playmaker - but the Parisians gained a first-leg lead to take to London next Tuesday when David Luiz turned a free-kick from Lavezzi into his own net just after the hour mark.
The visitors tried to ensure PSG only had a one-goal advantage as they defended deep in the closing stages - but a magical run from Javier Pastore in stoppage-time saw him jink past three Chelsea players in the box before steering a low drive past Petr Cech at his near post to make it 3-1.
"It was a horrible time to concede," Cahill told Sky Sports 1HD. "It's a sloppy goal and unlike us. It's a big blow at 2-1.
"It was difficult to come here; 2-1 would have been okay to take to Stamford Bridge. It's devastating."
Cahill's boss Jose Mourinho was more scathing in his assessment of the defending.
"He (Cahill) says sloppy. I say ridiculous," he added. "We played against a great team, full of good players especially attacking players.
"You would expect them to score fantastic goals. Not the goals they scored.
"The third goal was sloppy, Gary uses that word, but for me, ridiculous."