Oxlade-Chamberlain has vowed to do everything he can to make sure Arsenal finish in the top four for a 16th consecutive season.
He told arsenal.com: "Everyone in the Premier League feels pressure to get results," he said. "It is part of being a footballer. We have to take that in our stride because we know we have the characters to deal with it.
"The Swansea result is a good start. But we can't look back, we have to look forward at what we can achieve. That will be important for the run-in. So it is a matter of taking it step-by-step.
"We knew it would be a hard game. But we had to take everything from Wednesday's win at Bayern and use it in this game.
"We have always had belief in ourselves. Obviously there have been some hard patches. But wins like the one at Swansea affect the confidence in a positive way. We have to take that into the next game and look for three points again."