The Hawks were the better side during the Boxing Day derby against Eastbourne Borough at the Enclosed Ground, according to boss King.
They failed to take their chances, however, and Eastbourne left with all three points thanks to Yemi Odubade’s penalty.
It means the Hawks remain without a win in the League and King felt it was a big chance missed.
The manager told BBC Sussex Sport: “We dominated the whole game. We had most of the possession and I’m gutted because it was a soft penalty we conceded.
“I came in at a difficult time. You’ve got to try and build a side a quarter of the way through the season with players already contracted at other clubs.
“You’re left trying to galvanise a group to stay in a division that is very competitive. I don’t think there is an outstanding team in the division but it is very even - it’s fine margins.
“You’re looking for the light at the end of the tunnel and I felt that Boxing Day was the potential first three points.”
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