After nine years without silverware, Arsenal finally tasted success courtesy of a 3-2 victory against Hull City in extra-time of the FA Cup final at Wembley in May.
Lifting the FA Cup trophy has only increased the appetite for more silverware, with Arsene Wenger's men now targeting their first league title since 2004.
And Jenkinson, 22, said Arsenal are capable of competing for top honours on the back of Alexis Sanchez's high-profile arrival.
"Once you’ve got one, want to experience it again," Jenkinson told the club's official website.
"Everyone was over the moon with winning the FA Cup - it was such a big thing for us all.
"Fingers crossed we can compete on all fronts this season. We have the squad and we are signing players like Sanchez, so I don’t see why we can't."
