The Ligue 1 leaders were beaten for the first time this season in all competitions thanks to goals from Nuno da Costa and Stephane Bahoken, either side of a Kylian Mbappe strike.
PSG had 73 per cent of the possession and 29 attempts but rarely looked like denying Strasbourg a famous win after going 2-1 down in the 65th minute, when Bahoken raced through to score after a goal kick was flicked on by Nuno.
Pastore was frustrated to lose in such a manner but hopes the result serves as a wake-up call for the rest of the season.
"Strasbourg had two chances," said the midfielder. "We weren't at 100 per cent from the start. We tried but we weren't able to score the second goal.
"It's no accident; it's because they were very good. They had a very good defence.
"The goal is to finish first at the end of the campaign. We've taken a knock that will help us for the future.
"Today, we paid dearly for two moments for which we weren't focused."
Centre-back Marquinhos also blamed PSG's lack of concentration and says they must learn to be more effective with their opportunities.
"We couldn't take advantage," he said. "We conceded two stupid goals. We were lacking concentration.
"Strasbourg played their game. It will help us for the future.
"We had chances but we didn't know how to be efficient."