Maribor coach Darko Milanic felt Rangers' decision to replace Steven Naismith at half-time was the turning point in the match.
Kyle Lafferty took Naismith's place for the second half with Rangers' having led 1-0 at the break.
But goals by Agim Ibraimi and Etien Velikonja gave the Slovenian side a first-leg advantage.
"I was very surprised about the change because it changed the match completely," said Milanic.
Naismith had been booked in the first half and Lafferty was played in a slightly more advanced position when he came on.
"We had space in midfield and a lot of movement after that," added Milanic. "It changed the game."