Craig Gordon drew the plaudits from both managers after his penalty shoot-out heroics saw Hearts into the Scottish Cup quarter-finals.
Scotland goalkeeper Gordon was the hero after saving from Ayo Obileye to send the Gorgie outfit through 4-3 on penalties following 120 minutes of goalless action, and Hearts boss Robbie Neilson said his presence in goal was a huge factor.
He said: "If I was an opposition player stepping up and Craig Gordon was in goal I would have a squeaky bum, that's for sure!
"I thought they all struck their penalties really well. We asked them to go and pick their spot and go and hit it and to their credit they did that."
Livingston manager David Martindale added: "It's a sore one. I feel sorry for the players.
"I don't buy into the idea that penalties are a lottery. It's about ability and mentality. Craig Gordon is an imposing figure in the opposition goal."
Hearts had dominated long spells of possession, but lacked a cutting edge in attack, with Barrie McKay, Peter Haring, Ellis Simms and John Souttar all denied by Lions goalkeeper Max Stryjek.
Livingston did strike the post in the second half through Scott Pittman, but Hearts - losers of the delayed 2020 final to Celtic, also on penalties - prevailed.
Neilson said: "It was a tough game and we knew it would be.
"Livingston are a very good team, they have caused a lot of upsets this season.
"We're off the back of eight games in 26 days, we have used the least amount of players of anyone in the league during that spell.
"Some teams have used 13, 14 players more so it was always going to be tough to get through it. The boys will get a few days off now and hopefully that will bring the energy back."
Martindale was frustrated his side could not capitalise on their opportunities.
"I thought over the piece, we gave up a lot of possession, but we dealt with balls in the box," he said.
"Max had a save from a glancing header. We had two outstanding chances in the first half through Bruce Anderson and then we had one in the second half with Pittman when it hit the inside of the post and fell back into Craig Gordon's arms.
"We created the better chances, albeit Hearts dominated possession."
