Two goals from Lukas Podolski and an early opener from Olivier Giroud helped the Gunners bounce back from their opening day defeat to record a 3-1 win over Fulham at Craven Cottage
Following that loss, the Gunners have since hammered Fenerbahce in the first leg of their Champions League qualifier and recorded a 3-1 win over Fulham at Craven Cottage.
Jenkinson says the whole squad were itching to set the record straight after losing to Paul Lambert's men, and believes the team have performed "exceptionally" in their follow-up fixtures.
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"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, Jenkinson could be drafted into play at centre-back, a position he feels capable of playing, and the 21-year-old 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 added.
"I'd probably say my main position is right-back but I guess that [versatility] is a strength of mine."