The Gunners will head into Tuesday's Champions League playoff second leg against Fenerbache with a healthy 3-0 advantage.
Things looked dire for Arsenal after losing their first domestic game on August 17 as critics savaged the London club for their lack of transfer activity over the summer.
But a terrific performance in Turkey followed by a comfortable 3-1 win at Fulham has seen Arsenal's confidence rise.
"Especially when you're playing for Arsenal, you don't want to lose any game and you're not expected to," Jenkinson said in the lead-up to the clash with Fenerbahce in London.
"So to lose the first game at home (versus Aston Villa) was very tough and I think everyone took it personally and looked at themselves and thought, 'that isn't good enough'.
"We've gone out since and the last two games I think we've performed exceptionally and everyone's lifted their game which was important.
"We've got to continue to do that if we're going to be successful this year."
With Thomas Vermaelen and Laurent Koscielny both injured, regular full-back Jenkinson has played both in central defence as well as his natural position and he sees his versatility as a positive.
"Since I've been young I've always played in different positions across the back four and all through my youth career I've played centre-back, so it's something I'm capable of doing," Jenkinson said.
"I'd probably say my main position is right-back but I guess that (versatility) is a strength of mine."
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