The Dark Blues are still looking for their maiden cinch Premiership win of the season while Livi picked up their first point.
McPake handed a start to on-loan Celtic striker Leigh Griffiths, with the 31-year-old having opportunities but could not find a way past Livi keeper Max Stryjek.
He said: "I thought we created some clear-cut chances in the first half and their keeper made a good save from Leigh after the break.
"But, at this level, the players now realise if you create those kinds of chances, you have to take at least one of them. That's what you must do when you're on top.
"Of course, the first goal is massive in games. If we had got it with the crowd behind us, we would have gone on to win the game but that's all ifs and buts.
"In the Championship, you maybe get another four or five clear-cut chances but at this level it's different. We need to start winning games."
McPake, though, was pleased Griffiths managed to see out the game in what was his first competitive match of the season.
He added: "I'm delighted he got through the 90 minutes. It's always a risk when he hasn't done that for so long.
"That will have done him the world of good. He's got a wee bit to go in terms of sharpness but we'll work on that this week.
"He's been working really hard at Celtic since coming here so that's why he was able to get through this 90 minutes."
Livingston boss David Martindale admitted the game was not a great spectacle but he was just happy to have secured a point and a clean sheet.
He said: "It wasn't the greatest of games to watch for the neutral.
"It was blood and guts, both sets of players were getting stuck in for it.
"Dundee probably had the better chances overall but I think we had a few ourselves to have something more.
"We got a clean sheet and a point so we have to be happy."
Livingston's day was blighted by a first-half injury to Craig Sibbald which saw him stretchered off and Martindale admitted he was gutted for the player.
He added: "Sibbs has been taken straight to hospital. It looks like he has caught a stud in his ankle."