The Minstermen, who take on second-placed Port Vale as they chase their first league win in four matches, were also edged out of the FA Cup after extra-time at AFC Wimbledon on Monday.
"Of course it concerns me," Mills said. "I'm a football manager and I want to win games and that's what I'm judged on, so it is a concern and we have to look at reasons why.
"You can only go on for so long saying we're creating chances and as long as we keep doing that it's positive.
"Well, we've got to the stage now where we've got to put these chances away. You cannot keep saying the same thing every week because people get fed up with it and think it's an excuse.
"It's not an excuse, it's a fact, but as manager I've got to do something about it and pick a team that is right to win at Port Vale, so concerned? Yes. Overly concerned? No.
"Are we playing well? Yes. We've had one bad game, so performance-wise I think generally we've been very good, I really do.
"Result-wise? No, we haven't been getting the results, but as long as the performance is there, that belief and commitment to our jobs then, while I'm fully aware of it, I feel we will come through it and start picking up results."