At the weekend, Boro slipped out of the FA Trophy with a whimper at Workington, having not registered a shot on target.
But tonight's clash gives them the chance to respond in style when they entertain rivals Whitby Town at the Flamingo Land Stadium.
Kittrick said: "We didn't play well at all on Saturday, but we have the chance to put that right against Whitby.
"It is about what we do as a group now and how we respond from Saturday's disappointment.
"We all know that this is important for the fans, you can feel it and see it.
"The lads know that they have to go out in these games and do that bit extra for the supporters.
"There is local pride and bragging rights at stake, we'll be doing our very best to make sure our supporters are the ones cheering at the end of the night."