Ross County won 2-1 at Dens Park leaving the home side one point behind St Johnstone and eight behind the Staggies.
Dundee took the lead through Zak Rudden but were undone by slack defensive play.
"The decision-making from the start wasn't good enough," McPake said. “Both goals are ridiculous. They are nothing short of shambolic.
"I will take that on the chin as I pick up the team. I will take my share of the blame, or all the blame, if that's what gets thrown at me."
With the win, Ross County can begin looking to the top six.
"We're four points from sixth place, and I know the teams above us are doing well,” manager Malky Mackay said. “But we just have to keep the momentum going.
"After the winter break, we've had great results. We can play against anyone in the league and do well and score goals. We defended royally and it gives us a springboard to attack teams."
Regan Charles-Cook was amongst the goals once more, taking him on to 11 in the league so far, with Joseph Hungbo grabbing the other.
Mackay said: "Regan is a calm boy, a terrific lad and there was no need to try and lift his head after the penalty because he caused Cammy Kerr an awful lot of problems down the right-hand side.
"His finish was just like the one against Dundee United – high into the net. That's six goals in seven games and he's doing so well for us. It was a real team effort but a quality finish from him.”
He added: "It was a steelier-looking Dundee team. They put their new signings in. We knew they would look for balls into Zak Rudden.
"In the first 15-20 minutes we didn't win too many second balls and they scored. After that, we stepped onto the game.
"I was really happy with the second half, the way we controlled the game. We could have scored a couple more. We missed the penalty, but looked really, really fit and aggressive.
"Especially coming here, a lot of people were talking of this being a six-pointer."