Alexis Sanchez and Mesut Ozil scored either side of an Alvaro Negredo equaliser on Monday as Arsenal secured a 2-1 Premier League win at the Riverside Stadium.
With their top-four hopes still alive, Oxlade-Chamberlain acknowledges that bouncing back from their recent sorry slump was crucial for Arsene Wenger's men.
"What we've done hasn't been good enough. We need to take responsibility for that," he said.
"We needed to go out and get back to the basics and that's making sure our commitment levels were right.
"It's a massive honour to play for Arsenal and maybe those levels have slipped."
Laurent Koscielny also talked up the importance of the Gunners' win on Teesside, but admitted they were still below their best.
"It was important. We were in a bad situation and we needed to come back with our quality," he told Sky Sports.
"It was not perfect but I think it's good to come back with the win. It's good for the confidence. It'll come back slowly but it was very important to win."
Ozil's 71st-minute winner put Arsenal within seven points of fourth-placed Manchester City, and Wenger's men have a game in hand.
Arsenal now turn their attentions to the FA Cup, facing Manchester City in the semi-finals on Sunday.