The home team were on top after Danny Grainger gave them the lead just before the break but the Lithuanian’s slip allowed Marc McNulty to fire the First Division side back into the game.
“He showed character,” McGlynn said. “He made a mistake and cost us a goal in a game where we should never have got ourselves into that situation.
“We deserved to be in front at half-time, and I thought as long as we stayed disciplined and didn’t make a mistake I couldn’t see them coming back into it.
“But we made a mistake, then everyone had to show a bit of character.
“Marius had to get his head up, and to be fair to him he scored two at the other end. You look for leadership from the team captain.
“It was a pleasing performance, we’re in the next round, and we’ve had back-to-back victories. It could have been more comfortable. Three-one dioesn’t show a true resemblance of the superiority we had.”
Livingston manager John Hughes was pleased with aspects of his team’s play, but argued they could have done better. “Our shape was good, and, tactically, we were good but we’re a better passing team than that,” he said.
“I’m disappointed with the way we conceded the goals, but I thought we had the best player on the park in the wee boy [Stefan] Scougall. I thought he was absolutely outstanding.
“We gave Hearts a fright, but we couldn’t hang on to it long enough. But that will give us a platform and something to go and play from.”