The France forward scored twice in the first half as the Gunners put the midweek Champions League defeat to Bayern Munich behind them. Czech playmaker Tomas Rosicky converted a well-worked third before defender Laurent Koscielny headed home from a corner just before the hour.
Sunderland, who meet City in the Capital One Cup final at Wembley next weekend, grabbed a consolation through a 25-yard drive from substitute Emanuele Giaccherini - but Poyet's men remain deep in relegation trouble.
He said: "I am not accepting this defeat. We were poor in many ways and were second best in everything, Santiago (Vergini) was not the only one.
"Now no-one has put themselves on the teamsheet for next week, they all had a great chance to show me but everything I had in mind went in 90 minutes. Now I have to start from zero
"Arsenal proved again that they can beat anyone but sometimes players pick the team for you but now I have a few options for Wembley.
"There are plenty of similarities between the way Arsenal and Manchester City play for me to ponder on."