The Gunners suffered a demoralising 4-0 defeat at top-four rivals Liverpool in August but have begun to get their season back on track with convincing wins over Bournemouth in the league and FC Koln in the Europa League.
Arsene Wenger's side entered today's game having already defeated the Blues in the FA Cup and Community Shield this year but failed to find the breakthrough in an entertaining contest at Stamford Bridge.
"We needed that against a top team," Ramsey told Sky Sports News afterwards. "In recent years we have struggled here but we are able to compete against the best. We showed that we can create chances and on another day we may have nicked that.
"We needed that after the Liverpool game. We played in their half, higher up. We showed that we really wanted to get a result today and we got one here.
"We are in a good place, we just have got to keep building now on this. We dropped a few points already so it was important to come here and get a result."
Next up for Arsenal is a home encounter with Doncaster Rovers in the EFL Cup, while their next league encounter is with West Bromwich Albion a week tomorrow.