Chelsea twice came from behind to cancel out strikes from Bradley Barcola and Ousmane Dembele, with Malo Gusto and Enzo Fernandez scoring for the visitors.
However, a 15-minute spell saw PSG score via late goals from Vitinha and a brace from substitute Khvicha Kvaratskhelia.
"Looking at the game overall, it was fairly even after 75 minutes and then the final quarter-of-an-hour sort of ran away from us," said James. "We didn’t finish the way we wanted to and that’s disappointing.
"This is the Champions League and anything can happen. This is the greatest competition in club football and many teams over the years have turned ties around, from bigger deficits than this one facing us.
"We need to put this one behind us and look forward now. We need to react, the game didn’t go our way here but it’s only half-time.
"There’s lots to learn from this game, we know we’ve made it super difficult for ourselves for the second leg but the game is not done, far from it.
"This is a Champions League tie, the best competition at club level, over two legs and we need to reset and go again.
"I’ll say it again to everyone but especially the Chelsea fans. The game is not finished, it’s only half-time. And we will give our all in the second leg."