Manager Nigel Worthington insisted York must find their ruthless streak after they came from two goals down to salvage a 2-2 draw against Cambridge.
The Minstermen could have scored twice inside the opening minute but it took goals from Jake Hyde and Wes Fletcher to cancel out earlier strikes from Tom Elliott and Kwesi Appiah.
York have now drawn all three of their Sky Bet League Two games but Worthington feels they could have had maximum points.
He said: "We had two or three chances inside the opening few minutes and we have got to get sharper. It's a hard-earned point but it is two points dropped. We should be on five points, and, if we do our job properly, we could easily be on nine.
"We want to entertain but there are different ways of doing it. We showed character and a strong personality to get something from the game. We had a chat at half-time to sort things out and for 43 of the 45 minutes in the second half we were camped in their half.
"I've got to give my players credit as the quality was good, we created chances and we competed - that's how my sides have to play. I can't question the performance but we can't concede goals like that. We can't give teams the lead and expect to win games."
Cambridge boss Richard Money admitted he was pleased with a point despite letting their commanding lead slip at Bootham Crescent.
The U's have taken four points from a possible nine from their opening three games after promotion back to the Football League and Money admits he is happy with their haul.
He said: "It's an away point in a really tough game - at the end of a tough week, and in the middle of a tough period. We've got four points from the first three games, and given the fixtures we've had and the travelling we've had to do, I don't think that's a bad return.
"People will look and say we've let a two goal led slip away, but I don't think you can say that - because 2-2 was the least they deserved from that game. It's a learning curve for us, because they were very, very good.
"It was only the fact that we were very good in the front half of the pitch that means we've come out of here with a result, and I think four points from our first trio is a pretty good effort."