The Spanish giants progressed on the away goals rule following tonight's 1-1 draw at the Camp Nou, with the tie finishing 3-3 on aggregate.
Defender Pique believes that his team were superior during the first leg, and the better side overall.
"I think Barca has shown a lot of quality in the six years and I think we deserve it again to be in the semi-finals," BBC Sport quotes him as saying.
"[Paris Saint-Germain] are very strong with good quality but I think we deserved it. In the first leg we deserved a little more and tonight we're very happy to have qualified."
"It doesn't matter if [Lionel Messi's] a little bit injured he can change everything," he added.
"We are very proud and lucky to have him in our side. He's our reference as a striker - he can score, he can pass he can do anything and everything."
Javier Pastore put PSG 1-0 up on the night before the Spanish international netted the decisive goal.