On the pitch, his side produced another professional performance to exorcise any relegation fears.
The win over Dundee was their fourth in five games and they have been the form team of the bottom-six split.
Armstrong's 31st-minute penalty - his second in two games and awarded for Seb Palmer-Houlden's foul on Liam Donnelly - put Killie in the driving seat but they should have been ahead before that as Bruce Anderson rolled a big chance wide.
Dundee enjoyed more possession but were struggling to do much with it until the 76th minute when Lyall Cameron got on to Oluwaseun Adewumi's pass and squeezed the ball past Kieran O'Hara.
Parity lasted mere seconds though, as Kilmarnock went up the left-hand side where Donnelly crossed to Anderson, flying through the air to power his header into the net.
A lot of Killie's chances came from set-plays and the goal that proved to be the winner came from a corner as Deas headed in Armstrong's curled delivery.
There was still time for Cameron to twist and turn on the edge of the box, firing a lasered shot into the bottom corner, but it would not be enough.
Kilmarnock remain ninth, safe with two games to play, while Dundee sit 10th, two points above Ross County - who they play on Wednesday night.