Enrique admitted that defensive lapses cost them crucial points in their push to stay top of Ligue 1.
PSG looked in control early on when Bradley Barcola opened the scoring, but the match turned dramatically as Strasbourg struck three times in 23 minutes through Joaquin Panichelli's brace and a goal from Diego Moreira.
Goncalo Ramos pulled one back from the penalty spot before substitute Senny Mayulu rescued a point late on.
The draw extended PSG's inconsistent run, with only one win in their last four Ligue 1 matches, a worrying trend for Enrique, whose team had previously gone 19 games with just one defeat.
The three goals conceded marked the first time PSG had shipped so many in such a short spell since their 5-1 loss to Lille in April 2019.
"No coach takes pleasure when he concedes three goals. It's impossible to be happy," Enrique said after the match. "We must use all the data available to analyse what went wrong and improve.
"Strasbourg are one of the best sides in Ligue 1 right now; they play brave, attacking football, and we suffered because of it."
Despite their defensive troubles, PSG remained top of the table on goal difference, with an expected goals tally of 2.7 compared to Strasbourg's 2.2. The champions were without Ousmane Dembele due to injury, although summer signing Khvicha Kvaratskhelia returned from the bench to make an impact.
"I'm trying to manage the minutes as best as possible for the team," Enrique added. "It's a demanding schedule, and we have to balance things before and after international breaks."
With key fixtures ahead, Enrique will demand an immediate reaction from his players as PSG aim to tighten up at the back and maintain their lead at the summit of Ligue 1.