A controversial refereeing decision saw the away side awarded a penalty on the hour mark, which Jamille Matt converted, after Jai Rowe was adjudged to have committed a foul.
With United trying to force their way back into the game, the away team added a second through Ebou Adams.
Cox said afterwards: "It's another defeat, but I'm really proud of the boys with their effort, determination and the way they handled the situation with the refereeing decision (for the penalty) going against us.
"Yes, we did get a little bit feisty at the end but that's what I expect from my players when we're battling.
"In the first half, we sat in and tried to play counter-attack football. We had a couple of opportunities and their goalkeeper made a couple of good saves.
"Harry Davis had to come off after being elbowed in a poor challenge, which the referee didn't see. We had to change it and gambled a little bit.
"In the second half, we came out and the referee made a decision for the penalty that cost us the game really, because they seemed to happy to come here and get a point at that stage.
"We were then 1-0 down and tried to make some changes by pushing forward, but were done by a poor goal, I must admit, at the far post.
"We still went for it and battled over the whole game, showing passion and a bit of quality, but we just didn't have that luck in front of goal.
"We let everybody down last week, but the fans saw passion in the way we performed today. If we can play like that every week, at that tempo, with the quality we had at times and a bit of belief we'll be fine this season.
"We showed a lot of spirit today and I believe if we had a bit of luck with the refereeing decisions, we could have got more than we did."
Skipper Davis' head injury was a recurrence of the one picked up last month, which ruled him out for a couple of games.
Cox added: "He was caught with an elbow and it's a bad one, not looking good, as he had the injury there previously before and was out for a little while with that.
"We also had a lot of illness. Myles (Hippolyte) managed to get off his sick bed, while Beest (Alfie Beestin) has also been struggling and that's why he didn't start.
"Ross (Millen) wasn't well enough to play, while there were a couple of others this morning who have got through the game. We'll send them home, and make sure they do the right things there.
"We'll not feel sorry for ourselves though. We'll dust ourselves down and prepare for a tough game away at Barrow on Tuesday."
See much more from Neil Cox and Manny Onariase on iFollow Iron.
