Chiellini is pleased with Italy's reaction to steal a point from Paraguay, but feels it should have been three points.
The Group F opener ended 1-1 at Green Point after Antolin Alcaraz gave the Albirroja the lead, before Daniele De Rossi struck back in the second half.
And there is an element of regret from the defender.
"The goal we conceded was a shame from a set piece as it conditioned the game," he told Sky Sport Italia.
"With all respect to Paraguay I don't know how they would have scored because we shut them out.
"But I liked the way we recovered the game and we deserved more than a point based on how we played.
"It's a shame because it should have been different.
"In the second half we were much better, I think a 4-4-2 gives us more balance and makes us compact, we were also better covered."
Gianluigi Buffon came off with an injury, but Chiellini doesn't feel it warrants too much concern.
"Buffon? I don't think it's anything serious, but the doctor will say something because he knows more than me.
"In any case we are satisfied because we put pressure on them, Paraguay are a tough team."
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