Ian Baraclough was delighted to mark his first match in charge of Motherwell with but acknowledged that on another day key decisions might have gone against his team.
The home team were reduced to 10 men in the 19th minute when captain Steven Thompson was shown a straight red card by referee Alan Muir for a marginally late challenge on Motherwell's Mark O'Brien.
And, in another close call, the officials decided Kenny McLean's header that thumped off the crossbar and flashed down near the goal-line did not cross the line.
"It's one of those that happens very quickly," said Baraclough of Thompson's dismissal.
"The referee has to make a decision. He saw the big guy coming in from the side and Mark O'Brien winning the ball first and it may have looked late.
"It's one of those challenges that front men have the right to make but if they mis-time it it can have the consequences that it had. It could have gone the other way."
And on Buddies midfielder McLean's header, the Englishman told BBC Scotland: "I thought it had bounced off the line and hit the net, but it was obviously the power of the header that shook the bar that shook the net.
"We switched off a little there. We worked hard to get the three points and it was a delight to see the Motherwell fans behind the goal celebrating.
"It tops off a really good, positive week for us. The players have worked really hard. The tempo in training was good. That can give us a little bit of confidence.
"We did a little bit on the shape, tried to move the ball a little bit quicker and get the players that could change the game on the ball as soon as possible, but that goes out the window when they go down to 10 men."
The Well boss said John Sutton's goal 18 minutes from the end was "fantastic".
"There won't be too many team goals better than that this weekend, which was a delight to see," he said.
The defeat means caretaker boss Gary Teale's side remain at the foot of the Scottish Premiership, a point behind Ross County and now six behind Motherwell.
"It seems to have been the story of our season so far, just these hard-luck stories," said Teale when asked about the red card and the McLean header.
"I didn't see it too clearly but it was a 50-50 ball," he said of the sending off.
"For me it was a coming together. If he's got it right, then fair play to him. If he hasn't, then it's something we'll maybe look to appeal because he is such a big player for us."
And on whether McLean's header had in fact crossed the line, Teale added: "Unfortunately we can't have goal-line technology up here because we can't afford it.
"Hopefully the season will start turning around for us."
Despite the result, Teale was upbeat about other aspects of the match.
He added: "I was so proud of the team. In football, you don't get anything unless you work for it. In terms of how much passion the boys showed for me today, I am over the moon.
"For me, for a professional footballer, hard work and desire is a given.
"I was delighted with how resolute we were, with the shape we had to go to when Steven got sent off."