Illustrating the fine margins of the game was the fact Dundee had several chances to score an equaliser even after Ian Harkes had given Dundee United a late lead.
The strike proved decisive as McPake’s side failed to capitalise on their late opportunities. It meant he was the one faced with having to explain the defeat to his club's supporters in media briefings afterwards.
Dundee are still searching for a first win in the league this season and later dropped to the bottom of the Premiership table on account of Livingston’s win over Celtic. Dundee hosts champions Rangers on Saturday and have now gone successive games without a goal.
“Both teams could have won that game today on the basis of chances,” said McPake. “I think we had the clearer cut ones – any one of us could have been standing here on the back of a 1-0 win.
“The game settled in the second half and we got to grips with what they were doing. It became an even contest and one goal was going to win it – unfortunately I am gutted it was them who got it.”
Leigh Griffiths was given another 90 minutes after playing all of last weekend’s 0-0 draw with Livingston. The on-loan Celtic striker came close to giving Dundee a first-half lead with a head and half-volley. He has still to open his account in his second spell at the club.
“Leigh will score goals,” said McPake. “There is no doubt about that. He is down there gutted but so are every one of my players and staff.
“We do not believe we should have lost this game. But we have and we need to move on.”
Dundee have a Premier Sports quarter-final tie against St Johnstone on Wednesday night.
“We can’t dwell on it,” said McPake. “It is great we have a massive match coming up. No disrespect to the Championship but last year we could have been going to Ayr United in midweek and now we have St Johnstone in a League Cup quarter final and then Rangers at home on Saturday.”