The Magpies' Under-23s recovered well from the blow of an early Aidan Connolly goal and former Celtic defender Stuart Findlay headed them level early in the second-half, although that wasn't sufficient to preserve their 100% winning streak in the build-up to the new campaign.
Beardsley told United's official website -
"To be fair to [York], they started off really well and put us under pressure. At 1-0 at half time, they were definitely the better team, without a shadow of a doubt.
"But I think for most of the second half we were camped out in their half. Having got the goal early in the second half, you're hoping that you're going to go on and win.
"There were a few tackles flying in, but that's men's football. With all due respect to York - Jackie's [McNamara] a good man, Simon's [Donnelly] a good man - it is going to be physical for them, and they have to do that sometimes.
"Fair play to York - they played some good football at times. They're fighting for their lives in terms of playing in the National League and then hopefully back in the league, so we always knew it would be our toughest test."