Mills believes the result flattered the visitors with Jack Redshaw scoring twice in the final five minutes with York pushing for an equaliser.
The Minstermen boss highlighted chances that fell to Patrick McLaughlin and Daniel Parslow as City failed to add to Jason Walker's first-half penalty.
"When I look back at what we did at the start of the season, we had chances but we never took them," he said.
"At 1-1 we've had two unbelievable chances to go 2-1 ahead and we haven't taken them again and we've been punished.
"I can't legislate for my goalkeeper fresh-airing the ball completely when we go 2-1 down. The fourth goal with their player going through my two centre backs is diabolical. The last 20 minutes was awful as it's another game where we should have got something out of it.
"The quality of finishing which has been a downfall for us this season, for me, has cost us the scoreline. 4-1 definitely flatters them but I'm not happy with the way we allowed them to score four.
"I can't do anything about Inghy's (Michael Ingham) mistake but at 2-1 you've still got a chance. Then it was too easy for them to score two more and it was just disappointing and a bad day for us."