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Arsenal took an early lead through Martin Odegaard, but City equalised shortly after halftime with a powerful header from Erling Haaland.
Then Thomas Partey put Arsenal back in front, with goals from Myles Lewis-Skelly, Kai Havertz, and Ethan Nwaneri sealing the route.
“It’s a really tough result to take today,” Savinho said after the game at the Emirates Stadium.
“It’s a really hard scoreline to accept and one that we can’t go home accepting.
“We have got to lift our head now, and look at how we can improve and take it forward into our next games.
“When I arrived at this Club I said one of the great things is that, even though sometimes we might lose, every two days we have a new opportunity to right these wrongs.
“So now it’s about showing our talent and showing what we can do on the pitch and putting it right.”