After winning 3-2 in Paris and taking a 1-0 lead with an early Raphinha goal in the quarter-final second leg, Barca went down to 10 men when Ronald Araujo was shown a red card, before PSG took control of the match and secured a comeback win.
"Very frustrated. Very disappointed. It really felt like that we had full control of the game. Started with a one-goal lead, and then after 10-15 it just felt like we destroyed ourselves," Gundogan told TNT Sports.
"Yeah, (the red card changed the game). This is the Champions League. No matter who the opponent is, in such a tie, such an important game, going one man down so early... it's impossible, then you are out, unfortunately."
Following Tuesday's defeat, Barcelona manager Xavi Hernandez berated referee Istvan Kovacs and said his performance cost the LaLiga club a spot in the semi-finals.
Kovacs showed red cards to Araujo and Xavi, with five Barcelona players also receiving yellow cards.
Gundogan concurred with his manager's opinion on the referee, saying he should have won a penalty after being tackled by PSG's Vitinha in the box.
"At halftime, (the referee) didn't have such a bad attitude. I haven't seen any of the crucial actions on the replay, but it felt like he was very quick on the yellow cards for us," the German said.
"In the second half, I think I should get a penalty. He clearly kicks me with his leg - if not, I can continue running. If he doesn't kick me, I don't fall. For me, that's a penalty.
"That's what I told him, to at least have a check, and he gave me a yellow card. I don't know how it looks on TV - maybe my impression is wrong."
