The visitors went into the match without a win over any of the top six teams in the league this season, and memories still fresh of another domestic cup exit to a bottom-tier club.
Motherwell sealed the win when Henri Anier raced forward as the Dons were caught short following a corner, and he squared for Lionel Ainsworth to stroke home at the back post.
McCall said: "We had a hard couple of weeks after going out of the cup and lesser teams would have crumbled after what had happened.
"But I said at the time that we have some good strong characters in the dressing room and those are the times you have to stand up and be counted.
"We were getting flak, which was rightly deserved at the time, but those are the times you have to show a bit of steel and character.
"It gets a monkey off our back in terms of having not beaten a side in the top six this season. It's a good boost to come and take three points from what is a difficult place to come to.
Aberdeen counterpart Derek McInnes was happy enough with the performance if not with the result.
He said: "There's no shame in losing to Motherwell. They're a good team and you don't always get what you deserve.
"We lost a really untidy goal which gave Motherwell something to hold on to and, from that perspective, it feels a bit smash-and-grab."