Tony Watt appeared to be caught by Conor McCarthy but stayed on his feet to deliver a cutback which failed to find a team-mate.
Alexander felt referee Kevin Clancy should have awarded a spot-kick and was baffled at the explanation he received from the match officials.
He was a far happier man than after heavy consecutive defeats by Hamilton and St Johnstone, but disappointed with Clancy for several reasons.
He said: "We were told it was a foul but he had to go down. I honestly don't get that.
"You could even see the reaction from the opposition bench. They knew. We all knew.
"But I just want to focus on our performance. Tonight was so much more committed than Saturday. I was really pleased with the way the players responded.
"We have had a lot of criticism and rightly so. We had to stand up and take responsibility because we let ourselves and everyone down. But we certainly gave an answer."
'I'm not a tripod’
Alexander was also disappointed to receive a yellow card from Clancy for reacting to another decision, ten days after receiving two in their defeat by Hamilton.
"I felt like I was punished for trying to coach my team," he said. “I don't think we were any different to any other bench in any other game of football.
"I was respectful, didn't swear, didn't call anyone anything.
"I don't know if I'm meant to stand there like a tripod and not move. Everyone gets passionate about the game and that's all it was."
Goodwin takes the positives
Saints boss Jim Goodwin took the positives following a game that was rearranged when his club overturned the award of a 3-0 win for Motherwell after the original match was postponed because of a Covid-19 outbreak.
"I don't think either side did enough in the attacking third but I need to credit my backline as they defended really well.
"It absolutely could be a good point. People will talk about the injuries Motherwell have but we have our own problems.
"It's a positive result in the regard it was down as a 3-0 defeat on the card."