York City's 2-1 defeat against the Iron on Saturday leaves them 14 points behind leaders Barnet.
With eight games to go - including tonight's game-in-hand at Rochdale this evening - Hinshelwood said he thought their title chase was "over".
He told York Press: “Before today I didn’t think so [that the title race was wrapped up] and that was the message to the players.
“Barnet had the late kick-off and all we can do is put pressure on them, but by losing, I think it’s over now to be honest.
“All we can do is do all that we can to finish second in the league.
“They’re not going to drop the points and I can’t see us at the minute stringing what’s needed, eight wins.
“We show a grit and a determination one week and then we show that this week.
“Ultimately, the top teams are just relentless, they’ve got that determination no matter what."
As is stands, Barnet can win a record fourth National League title with four more wins - seeing them promoted on Good Friday at the latest.
But York have a chance to reduce their deficit with a win at Rochdale - a place where they haven't lost since 2002.