Hearts were denied by a mixture of resolute defending and another fine performance by Killie goalkeeper Cammy Bell, and when 90 hard-fought minutes had ended, the visitors found themselves ninth in the Scottish Premier League thanks to a first-half Liam Kelly penalty, conceded after Hearts defender Andy Webster had tripped James Dayton.
Hearts are away at Ross County on Saturday before hosting Edinburgh rivals Hibernian on January 3 and McGlynn is looking for his players to dust themselves down and go again before the SPL takes a break.
He said: "The squad is strong. That was just a wee hiccup.
"We will not beat ourselves up too much about it because we have to move on to Saturday and a big game against Ross County.
"We have two games before the break and it would be good to get six points from them."
Dayton had a fine game on the wing for Killie and tricked Webster with some fancy footwork into conceding the spot-kick.
However, the Englishman acknowledged it was some stubborn defending that helped them hold on to the lead and move the Ayrshire club into sixth place in the table ahead of their trip to Motherwell on Saturday.
"I enjoyed it but it was a bit nerve-wracking towards the end," he said.
"We were on the back foot a lot in the second half but we have brought in something this season that we maybe lacked last season, we maybe lacked a bit of fight and grit to see out 1-0 games and that's what we did against Hearts, which was good.
"We go into the next game confident and hopefully we can get another three points and push up even further."
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