The Gunners picked up their first victory in the Premier League on Sunday when they beat the Reds 2-0, thanks to goals from Lukas Podolski and Santi Cazorla.
"After the two results we had, they weren't ideal and like I said before the game, if we win at Anfield, it would be a big statement of intent," Jenkinson told Arsenal's official website.
"We've gone and done that and shown we mean business. It's a good result and we're really pleased with it. We'll move on to the next game, it's only three points and we want to push on from here.
"Maybe people were questioning us after the first two games, but we knew in ourselves that the goals would come and we've come to Anfield, which is no easy place to pick up three points, and we've won 2-0."
Arsenal drew their opening two league games and now have five points from three matches.