Hearts head coach Derek McInnes told BBC Scotland: "I'm more disappointed than anybody. We'd done so much to get ourselves in front, and we needed to enjoy being in front a bit more.
"We felt the goal was coming. When we were good, we were very good, we were polished, connected well, looked after it well. At times, we looked like a team at the top of the league.
"But there were too many moments where we were sloppy, anxious in our defending, the gaps were too big between us.
"We can't keep pulling ourselves off the canvas. With half an hour to go, I wanted us to carry a but more of a threat. We've got to remember we're up against a team who are bottom of the league with something to hang on to.
"We needed to hammer home that authority and we missed the opportunity to stay in charge of the game. Psychologically, in terms of giving away a goal, was we gave them a boost.
"Both goals were so poor to lose, not the type we ordinarily lose. Our combination play was good, we had plenty possession and shots, but behind all that, there was too many wee moments where we were guilty of giving up good opportunities.
"We go a point clear with six games to go. People need to remember that, I'm trying to keep myself in check with that. It's a missed opportunity today.
"We have to be honest and say a point is all we deserved, and it might be a really important point come the end of the season, so we're not going to get too hung up on it."
Livingston boss Marvin Bartley said: "I'm delighted with the players. They dealt with adversity really well today.
"When Hearts went ahead, we had to show some character and we did that in abundance. The subs came on and improved us, made us more solid and caused them problems.
"We have to hit these heights every week. Where we end up at the end of the season is where we deserve to be.
"We have to go again and do it next week. It's the most difficult thing in football, to have consistency, but we need to show it now.
"The mindset today was good, they went out and did what they need to do. Good teams and good players bounce back, and we showed that today."