"It was important the lads kept believing in what we are trying to do and they never dropped their heads, even when they didn't get the right results.

"We have come in every day and worked hard and showed today, with a little bit of fortune, we got the right result."

Dundee United boss Micky Mellon confirmed that striker Lawrence Shankland, who missed out again with an ankle knock, was out of Steve Clarke's Scotland squad for the upcoming Nations League double-header against Israel and Czech Republic.

Dyer, formerly assistant to Clarke at Killie and Scotland, believes Brophy, capped once, would be able to step back into the international set-up.

He said:  "Of course he could step up, but it's not up to me.

"It's not about me, it's up to Eamonn to do the best he can for Kilmarnock and that'll take him wherever it takes him.

"I want Eamonn to get back to what he is good at.

"Sometimes you have to understand as a player the team will always come first, but he has to work hard and he showed that.

"When he does that, he is one of the best strikers in the league."

Former Kilmarnock defender Mark Connolly missed a chance for United at 1-0, just before Brophy fired in Killie's second on the stroke of half-time, and Mellon saw the chance as a turning point.

He said: "I don't want to be one of those managers who bleats about what did happen and didn't happen.

"But I certainly feel that there was a wee bit of naivety and that we had to be clinical in those moments to give ourselves a chance of winning.

"We didn't take care of the details at important times, which you have to be able to do.

We found ourselves down 2-0 at half-time and I'm scratching my head as to how that's happened, because I thought we dominated most of anything that happened in the first half.

"But that's football at this level, you need to understand and get better at that.

"You'll get punished if you don't attack every moment, or if you think, 'That one might not be the one you'll get punished with'.

"Well today it was and that's a lesson for them."