The Tynecastle side produced a limp display as they lost 1-0 to the Rugby Park side. The result leaves them ninth in the table, just two points off the bottom of the Premiership going into the October international break.
Levein said afterwards: "We just didn't do enough to win. I look at the stats and we've probably got more possession, chances and all that but for me that's not what it's about. It's about having the balls to dig deep when we need it. Everybody was waiting on somebody else being the one who changed the game.
“Did they try? Arguably. Did they try hard enough? Absolutely not. I've been at this point in the last four or five weeks where my job when they are struggling is try and support them and help their confidence.
"We've got some light at the end of the tunnel with getting players back from injuries and my point to the players today was 'don't come knocking on my door if you're not selected in the upcoming matches’. Because there's been plenty opportunities handed out. That wasn't acceptable today. Whatever the stats say, it's still not what I want us to do at home.
"If they want to stay in the team they need to have enough to win the game. Lots of people have had opportunities because of injuries and if they want to stay in the team, they have to do better than they did today. There's a difference between trying and absolutely busting a gut and our supporters expect they absolutely bust a gut. They'll run and they'll point to their numbers and say 'I did this and I did that'. When it's difficult and when it's hard and the supporters are on you're back, you need a pair of balls. Too many of the players felt a little bit sorry for themselves. You could tell with their body language and that's the bit that makes me angry.”
Levein started with Sean Clare and Ryotaro Meshino as his two main central attackers after Uche Ikpeazu missed out with a hamstring strain. The manager explained his decision to start with no recognised striker when both Steven MacLean and Aidan Keena were both among the subs.
"Uche’s hamstring was tight on Thursday, he's played three games in a week for the first time in I don't know how long and he felt it tight. With everything else that's happened with injuries with Washington and Naismith being out, if we lose Uche for a period of time then it leaves us with next to nothing. So I made the decision yesterday that we've got the international break so it gives him time to get himself in top condition for the next match.
“Ryo’s played up front before. The position isn’t alien to him. Steven MacLean has played a lot recently. He can help us when he’s fresh but he’s played three games in a week. Aidan is untried and untested at this level but we brought him on to try and get us a goal.”