Jenkinson thinks that the only way to make up for the disappointment of last weekend is to bounce back and secure a top-four finish.
He told the club's official website: "I'm distraught, to be honest. I know this match's importance.
"In history, we've always tended to come out on top but it wasn't our day. We beat them at home and they beat us at their place. But it's really disappointing that we haven't at least picked up a point. I think in a couple of days' time, we'll get our head around this and realise that we've bridged a gap like that before and can do it again.
"Everyone is disappointed we lost, but we will be positive and we will come back from this. We've just got to work our socks off because we need to be in that top four at the bare minimum."
Arsene Wenger's side have now lost three of their last four matches in all competitions.