Spurs were overwhelmed as Emile Smith Rowe, Pierre-Emerick Aubameyang and Bukayo Saka sent Arsenal racing into a three-goal lead after just 34 minutes -- the fastest that has ever happened in the history of the north London derby.
Son Heung-Min struck a 79th-minute consolation for Tottenham, who improved a little after the break but the contest was long since over.
"I decided bad," Nuno said after the game. "Didn't make the right decisions. And I refuse to go much further than that. It's my responsibility. All I have to say, I'll say it to the players among us. Because [we] must solve the problem.
"I have a message [for the fans]. A message that we are disappointed because today was a special game for all of us, for our fans, and we didn't achieve the standards that our fans deserve.
"So my message is I promise we'll try to fix it. The only message we can say by words. After that it's work. What I expect, what I want is a totally different game in the next one."
Spurs goalkeeper Hugo Lloris said they were "smashed" as they conceded three goals for the third Premier League match in a row -- the first time Tottenham have done so since 2003.
"We lost complete control in the first half," he told Sky Sports. "We got smashed and then had a good reaction.
"It's frustrating and very disappointing. It's the moment to stick together and carry on. The players were ready but we lost a bit of control. We lost the balance in the middle of the pitch.
"When you concede three goals in each of the last three league games you cannot hide the problems. But we are professional. There is a long way to go. We need to stay calm."