The Steelmen were penalised by referee Euan Anderson when Callum Slattery attempted to stand his ground as Rogic competed for a high ball just on the left side of the box.
"But for that goal just before half-time I thought the players were excellent,” Alexander said. "I thought it was a cheap decision for the free-kick and then it’s quality from them to work that oppprtunity to score.
"These ones around the box and in goalscoring positions, they’ve got to be proper fouls and that wasn’t.
"That was a coming together of two bodies which happens all over the pitch.
"And I had already spoken to the fourth official about a few around the halfway line where I thought the ref set the bar at a certain level of contact which is fine.
"But then you’ve got to be consistent with the rest of it and that’s where I thought it swayed.
"You know referees and officials always interpret certain challenges in different ways, so you take your lead off the first two or three so we did.
"But then there was inconsistency from then on.
"In general I thought he managed the game well, because there’s a lot of pressure on officials here with the crowd, without a shadow of a doubt.
"I saw that for the first time here today. So I thought in general that he handled that well but I just feel that got that one wrong.
"But listen, we’re all human. I made mistakes today, my players did so it is what it is.”
Alexander, speaking to MFC TV, said he felt the game was “very competitive”, with both teams looking to win it.
He added: "We wanted to try and press them in areas we thought we could tun the ball over and not sit on the edge of our box all game which we certainly didn’t.
"But the way we came out second half, we didn’t feel sorry for ourselves, the compactness of our team was superb, they never backed down and it was great to see.
"You’re not always going to get results or the points but you can handle yourself in the right way and my team certainly did that today.
"You know Celtic will have opportunities as well because unless you park the bus then you’re going to frustrate but we didn’t want to do that today.
"So it was a risk involved. But the risk is if you score and you get chances, which we did, then it’s a risk worth taking.
"I think Joe Hart made a brilliant save down to his left at 0-0 which is a big moment in the game.
"But we had other opportunities where the final pass or the final shot just wasn’t right. But certainly we got into great areas today and I thought we affected the crowd for a lot of the game.
"I thought they were getting frustrated and I thought the goal was the perfect tonic for them to relax at half-time and sort of go in with a slightly different view.
"But, from that side of it, my players came out and competed in the second half just as well as they did in the first.”
Alexander said his players could take many positives from the game going forward.
He said: “But what we don’t want to do is to be plucky losers. That’s the last thing that we want to create here.
"We want to create people that are disappointed that they’re not getting something at Celtic and they are.
"But I want them to believe that this isn’t our only opportunity of getting points at a big club.
"We have to go into every game like that and if we do we will come out with the rewards more often than not.
"The manager here has done a great job but I thought my team was in it right until the final whistle. There was a bit of game management going on from them at the end.”