The Gunners were beaten 3-1 by Aston Villa on the opening weekend of the Premier League season on Saturday but were able to put that behind them by beating Fenerbahce 3-0 in Turkey in the first leg of their Champions League playoff qualifier.
"It wasn't the ideal start to the Premiership but we bounced back tonight," Ramsey told Sky Sports 1.
"We played really well as a team. We've been under a lot of criticism of late but it was vital that we stayed switched on and got a great result here, which we did.
"We look very comfortable now going back to the Emirates for the second leg."