Despite being pleased with the team's display in the capital, Britton admits that they still have work to do if they want to stay in the top flight.
"It is difficult against a side like Arsenal, but we showed great character to keep going," he told the club's official website. "We didn't fall away and lose the game by three or four goals, we kept digging in and got the equaliser right at the death.
"There's still a lot of points to play for, so we're not safe yet, but I think the performances over the last few weeks have been good.
"If we can cut out conceding silly goals and the defensive mistakes we make as a team, and continue to play like that, then I'm sure we will get the wins that we need."
Swansea return to action on Saturday when they entertain Norwich City in the Premier League.