City failed to regroup quick enough and the home side added a second just two minutes later. Proctor's shot hit the post and Peter Duffield found the net after it came back out.
Proctor had another chance 15 minutes later but couldn't find a way past Musselwhite.
Minutes before half time York thought that they had gone 3-0 up, but the linesman's flag denied Richard Cooper.
York came out after half time with 10 men behind the ball, trying to catch City on the counter attack. David Beresford and Ryan Williams were causing problems from wide positions but the finishing touch was lacking.
A triple substitution was made 20 minutes from time. Mark Greaves, who had earlier picked up a head wound, was replaced by Ben Morley, Beresford came off for Julian Johnsson and Rodney Rowe was brought on in place of Ryan Williams.
The change soon paid off as City pulled back a goal in the 72nd minute. Morley crossed to Rowe who turned and was brought down in the area by Cooper. The former York forward picked himself up to send ex-Tigers keeper Alan Fettis the wrong way with the penalty.
Rowe nearly found an equaliser 10 minutes from the end when he raced onto a backpass, but Fettis just beat him to it as they both dived in.
He then put a left-footed volley just off target before the fourth official indicated five minutes of added time.
However, City failed to make their pressure pay and came away with nothing.
Richard Cooper was stretchered off in stoppage time when Nicky Mohan's dangerous lunge left him on the floor. It was later confirmed that Cooper broke his leg in the challenge (read more here).
Brian Little said of the performance: "I suppose in the first half they had three or four good chances but I don't think they were overall better than us - we just defended very poorly. They defended a lot more solidly than we did.
"My team played with good passion at York and I can't fault them for that but until we win games away from home the fans are going to get frustrated."
Starting line-up (4-4-2): Musselwhite; Greaves (Morley), Mohan, Wicks, Holt; Williams (Rowe), Sneekes, Whitmore, Beresford (Johnsson); Roberts, Dudfield.
Un-used subs: Glennon, Van Blerk.