McGlynn could hardly believe his side took nothing from their trip to Rugby Park.
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 Clydesdale Bank 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."