Napoli came out victorious 2-1 on the night after goals from Piotr Zielinski and Fabian Ruiz but Angel Montoro’s 25th minute strike proved crucial as the Spanish side progressed after winning the first leg 2-0 at home.
Gattuso was unenthused by the delay tactics employed by Granada and the former AC Milan manager launched a scathing attack on Diego Martinez’s men.
“We conceded an absurd goal today, it was three against one in the box. I can’t remember any other chances for Granada. We have to be proud of what we showed," Gattuso told Sky Sport Italia.
“Those who represent us need to make themselves respected a bit more – if an Italian team played like Granada tonight, they would get slaughtered in all the papers. There needs to be respect, today they wasted too much time, three minutes at every opportunity.
“I’m angry not because we lost, but because there was very little play.”
Napoli will now turn their attention towards Serie A, where the Partonopei currently lie in 7th position and pressure is gradually mounting on Gattuso.
“Right now we need to get the players and the enthusiasm back," Gattuso added. "The players need to be calm, it’s me that people should be bothering here.
"I’m the one who’s most responsible. Now, we have to get to work, it’ll be important for us. The Napoli shirt is a heavy weight, but we need to be calm and give that little bit extra.”