The home side won 4-2 on penalties after being held by Jim McInally’s part-time Peterhead to earn another bonus point following their similar spot-kick success in midweek at Cove Rangers.
Paul McGowan hit the winning penalty while Andrew Nelson, Craig Curran and Michael Cunningham also netted from the spot, after Declan McDaid had missed.
For Peterhead, Willie Gibson and Aidan Smith both netted but Jack Leitch and Jamie Stevenson failed to hit the target.
Dundee coach Mackay, who stood in for manager James McPake whose wife was in hospital giving birth, said: “We’re obviously not pleased with the overall performance. It wasn’t good enough to be honest. Following on from the other night, we just looked a little bit flat and have lost that creative spark.
“The players worked hard enough but really lacked in quality.”
This was Dundee’s first home match after back-to-back trips on the road to Raith Rovers and Cove Rangers. Their trip north to Cove had brought a 0-0 draw and some criticism from McPake about their lack of quality in the final third of the pitch.
The hosts had a point to prove so began brightly. In 17 minutes, summer signing McDaid cut in from the left and his curling shot fizzed just past Greg Fleming’s far post which got the fans off their seats.
Then, at the other end, the part-time visitors almost took the lead in 26 minutes. Rory McAllister combined with Leitch whose left-foot shot from 20 yards went just past Jack Hamilton’s right-hand post.
But in 79 minutes, Peterhead substitute Ben Armour ought to have won it. He pounced on a mistake by the Dundee defence only to shoot straight at Hamilton who parried to safety.
Jim McInally, the Peterhead manager, said: “I’m very pleased with the lads overall for competing so well against full-time opposition.”