The home side saw an early Sam Foley goal turned on its head as County hit back twice in the second half through Iain Vigurs and Michael Gardyne.
The visitors were fighting for their Scottish Premiership survival, a goal they achieved thanks to the victory, while Motherwell were playing out the last of five post-split games which would be widely described as “meaningless”.
For Alexander, however, there is no such thing in football as he looks to demand the highest possible standards from a group of players he inherited after being hired to replace Stephen Robinson in January.
He said: “I hate that saying – nothing to play for. We’re in a brilliant job, representing a brilliant club, you’ve got your pride, three points, your club, your family, your team-mates – you’ve got everything to play for every single game.
"The players have been great over the past three or four months, but we’re talking just 30 minutes after a really raw result, so I can’t think too positively at the moment.
"We’ve done the job we wanted to do when we came in by staying up but there’s a bad taste in my mouth after today but that might be good for me going forward in terms of helping me clarify a few things in my mind.
“For example, if we’re going to be up and down mentally then that has to change. Professional football is so competitive and we need to have the highest standards every time. You’re not always going to play as well as you can but your application, your focus and your motivation should never waver and it did today, without a shadow of a doubt.”
Asked if the performance had made up Alexander’s mind about a some players and their long-term suitability, he said: “Possibly. I don’t think you make good decisions in anger so I won’t be doing that.
"I already have quite clear ideas about what to do but there were a couple of players who were on the fence and I’ll just have to see tomorrow where we go with that.”