The Magpies were beaten 3-0 by the Black Cats at St James' Park to increase their relegation worries in the Premier League.
"I think it's the worst week since I've been at the club," Gutierrez told The Mirror. "To lose like that at home is something that I feel will make all the team be sad. The city is sad - they did not enjoy.
"I have stayed at home all week. I haven't been out because of the result. It's the same with all the squad. What can you say to the fans because they ask you what happened? It's about action not words."
Newcastle continue their fight against relegation on Saturday when they travel to West Bromwich Albion.