Porto will travel to Turin for the second leg with a 2-1 lead after catching the Serie A champion cold twice at Estadio do Dragao.
Rodrigo Bentancur gifted Mehdi Taremi a Champions League goal with a terrible pass to goalkeeper Wojciech Szczesny after just over a minute, while Moussa Marega doubled Porto's advantage just after the break.
Juve rarely posed a threat in a flat display before Chiesa gave it hope when he struck eight minutes from time, with Cristiano Ronaldo denied a penalty right at the death in a miserable return to his homeland.
Pirlo thought Juve, which lost captain Giorgio Chiellini to a calf injury in the first half, struggled to recover after such an early setback in proceedings.
"The approach became wrong after the first minute. When you have conceded a goal like this it is normal to be a little scared, you lack the certainties that should never be lacking [at this stage of the competition]," the former Italy international told Sky Sport Italia.
"The boys are a little down, we conceded a strange goal, then the match they wanted to play was set up and it became much more difficult.
"The tiredness after so many challenging matches is there, it is not easy to keep the same pace, but it shouldn't have happened. Fortunately, we got back on track, now we will focus on the return [leg]."
Alvaro Morata has been struggling with illness and although he came on midway through the second half, Pirlo revealed the striker still felt unwell after the game.
"Morata was not well, he has not been at his best for a few days. He came on when he needed to, but after the game he felt faint, he was a bit on the edge," he said.
Star defender Danilo will be suspended for the second leg next month after he was shown a yellow card.