The 30-year-old striker scored his first international goal since Euro 2012 during Saturday's match in Berlin, as well as having a strike wrongly ruled out for offside.
Despite holding a two-goal cushion in the second half, the world champions collapsed as Harry Kane, Jamie Vardy and Eric Dier all found the back of the net in what was a remarkable fightback from England at the Olympiastadion.
Germany now face Italy in Munich and Gomez is wary of his side repeating the same errors against a country who have not lost in their last seven matches against Die Mannschaft.
"I think that we set ourselves up in the right way but in spite of that, it is perhaps natural to take your foot off the gas when you are 2-0 up in a friendly," the Besiktas striker, on loan from Fiorentina, told the DFB's official website.
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"It's just how it is. We gave England a lot of room and they are blessed with a lot of individual quality. We were stupid to have lost this game.
"We lost our way and left too much space, which England used well. They scored two goals from set plays. We knew they would be dangerous from those situations and they showed that."
He added: "We weren't good in the last 30 minutes and we need to look at that. We have to remain focused over the full 90 minutes, even if we are 2-0 up.
"We can't let it happen again as teams like England can take full advantage. In a major tournament, that results in you going home. That much is clear to us.
"Italy will obviously be a tough game as they have a good team and traditionally play very well against Germany. I think it's important to play well and get a good result to begin our preparations for the summer in a positive way."