Motherwell plan Liam Polworth red card appeal for bad language as Aberdeen 'respond in right manner'
Polworth was sent off for using foul and abusive language just three minutes into the second half, following a coming-together with Lewis Ferguson, with his team already trailing to Tommie Hoban's back-post header.
Alexander said: "He did swear, he admits that, but I don't think he was the only person who swore today. He says it was at the player who fouled him, so we will try to appeal it if we feel that we have grounds.
"I thought my team were superb today. We were a real good team today, and all we're trying to focus on is what we can control. That's our performance, our work ethic and our discipline as a team.
"I thought we deserved to be at least level pegging at half-time. We could have had a couple of goals from open play.
"It would have been easy to feel sorry for ourselves but we tried to continue to keep attacking players on the field and we did well in everything under our control. We can't do anything about anything else."
He said: "I thought we were good. It was important after a disappointing performance last week.
"We always aim to respond in the right manner. It was making sure we were robust and aggressive enough in our defensive work as has been the case this season and I think we did that.
"The sending-off makes things a bit more straightforward and I thought we used the width of the pitch well."