The retired centre-half says that while nobody can condone the Uruguay international's actions, the fact that the forward has apologised should be taken into consideration
Suarez was hit with a nine-game international ban and also suspended from all football-related activity for four months for biting Chiellini's shoulder during Uruguay's Group D clash with Italy in Natal on June 24.
Despite the striker's actions, Barcelona still opted to sign the 27-year-old from Liverpool for £70 million - a move that Puyol is fully supportive of.
"There is no justification for what Suarez did, but things like that occur when you lose your head – it can happen," the former Spain international told Fifa's official website.
"At any rate, he has apologised for it. He’s a great footballer, extremely competitive and scores a great deal.
"I think he can bring a lot to an attack that’s already brimming with quality. With Luis, we can be even stronger."
Puyol's retirement at the end of last season has left Barca with other issues to address at the other end of the field.
The 36-year-old freely admits that the Catalans have repeatedly failed to strengthen their back four in recent seasons but argues that it is particularly difficult for the Blaugrana to find suitable reinforcements given their propensity for playing a high defensive line.
"For some time now Barca have been looking for centre-backs," he said. "Then again, so has half of Europe, so it’s not easy – even less so for us, given our style of play.
"To represent Barcelona, it’s not enough to possess technique and the ability to come out with the ball, you also need to have pace, as we defend so far from our goal.
"When you look over your shoulder and realise just how far out you are, you feel dizzy sometimes!"