The Minstermen have collected 11 points from a possible 15 in their last five outings, culminating in last weekend's 2-1 win against Southend.
Parslow is undaunted by the trip to face the Daggers who themselves need a win to preserve their league status.
"We've just got to keep looking after ourselves because, if we do what we can do, we will be all right," he told the York Press.
"We are on a good little run at the minute. We have found our feet and I think it was just about getting that first result and the confidence has grown within the squad since then.
"It would have been great to have wrapped it all up on Saturday but teams are scrapping for their lives and picking up points."
Parslow added: "That's just the way it is, so we have to go to Dagenham and get a result."