Poyet told BBC Sport after the match: "I'm sure everybody will comment on the two goals but we tried hard, the players gave everything. We did not create enough but you cannot concede goals like we did today.
"It's a long week after two defeats but we've got plenty of time to make decisions. There is no other way other than to keep working, convincing the players and trying not to make mistakes and hopefully try to win a game. We made it difficult for Arsenal apart from the goals.
"I wanted to see the players today, to see them be brave and pass the ball and I think they were close. We didn't make many mistakes in the first seven games but in the last two games we made more than you expect in the whole season. We need to put that right."
Sunderland currently teeter just one point above the relegation zone, in 17th place.