The home side were unlucky as Nikolce Noveski appeared to be offside when he opened the scoring in the Group A World Cup qualifier, though goalkeeper McGregor accepted the goal was punishment for their lacklustre early showing.
Miller equalised just before half-time and substitute Jordan Rhodes had chances to grab a winner, but Craig Levein's side were also indebted to McGregor for some sharp saves in the closing stages.
McGregor told Sky Sports 1: "Am I right in thinking the goal was offside? Well, they've had a bit of luck there then.
"But the boys didn't start well and it's hard not to start well and then up the tempo.
"The 15 minutes before half-time and then the second half, we improved and created chances. If we'd started with the tempo we had in the last 15 minutes of the first half, it might have been different."
The result leaves Scotland on two points in the group following their goalless clash with Serbia and Vancouver Whitecaps striker Miller added: "It's not ideal, we set out to get six points and we've come away with two draws.
"We're bitterly disappointed because it was two home games and we've had good home form, but it's gone now.
"Saturday we felt we played well enough but tonight the performance was well below par.
"We need to play with a quicker tempo, we weren't up to speed in the first half and it took the goal to give us a little shake. The performance as a whole was not where we want to be and we paid the penalty for that."
McGregor insisted Scotland's qualifying hopes remain intact despite their two-point haul up to this point but acknowledged they will face pressure.
"I know (the media) don't think so and will be caning everyone again but we believe in ourselves, it's just unfortunate we didn't get off to a good start," he said.
"These aren't mugs we're playing, it's international football and every game is difficult."
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