Dunfermline were the last side to qualify for the last 16 when a late Chris Kane penalty secured a win away to St Mirren on Sunday that sealed progress as one of the three best runners-up at Championship rivals Queen’s Park’s expense.
Although St Mirren still topped the group on goal difference, the defeat meant they missed out on being seeded in Sunday’s draw.
Reacting to being drawn away to Rangers, manager Craig McLeish said: “I am disappointed from my point of view that we had a chance to win our group and be one of the seeded sides and the draw has not been good to us.
“I thought we were denied a goal, but we only have ourselves to blame unfortunately.”
Dunfermline head coach Neil Lennon was a happier man.
“I thought we played well in the last half hour and deserved our victory,” he said.
“A home tie is the most important thing, but Ross County have been phenomenal this season after a hugely disappointing relegation, so we will not be taking anything for granted.”
Aberdeen, Ayr, Dundee United, Inverness Caledonian Thistle, Kilmarnock, County and Stenhousemuir were the other group winners, while Dundee and Partick Thistle progressed as runners-up.
Celtic, Heart of Midlothian, Hibernian, Motherwell and Rangers were given byes to the last 16 as they are representing Scotland in European competitions.
While the Old Firm have been drawn against top-flight opponents, the other three take on Championship sides, with Hearts hosting Caley Thistle, Hibs at home to Partick Thistle and Motherwell away to Stenhousemuir.
The second-round ties will be played on the weekend of 15-16 August.
