The victory at the Emirates extended Swansea's unbeaten run in the Premier League to six games and lifted them up to seventh spot in the table.
Swansea welcome in-form Norwich to the Liberty Stadium next weekend and Britton says the players are focusing on picking up another three points as they look to secure survival as soon as possible
"We don't want to get too carried away, obviously Saturday was a great day for us," admitted Britton.
"We'll enjoy it for 24, 48 hours and then move on.
"We've got a very tough game against Norwich on Saturday so we'll just take each game as it comes. The aim at the start of the season was to stay in the league and we're still very new to it. We're only 18 months into it.
"We'll just take it steady. The main target is survival and we'll evaluate it after that."