Lovenkrands admitted that 10 man Killie had shot themselves in the foot with the sending off, but insisted that confidence had been buoyed by a professional performance by the Gers.
"It was the perfect start for us," Lovenkrands told BT.
"We got some self-confidence and, although they gave us a goal and got a man sent off, we did our job.
"We had the opportunity to relax a little in the second half and we have a lot of optimism going into the Champions League qualifier against FC Copenhagen."
Rangers' good start was boosted by rivals Celtic being held to a 0-0 draw by Dunfermline, but Lovenkrands has some sympathy.
"In the league there is pressure on us all the time," added Lovenkrands. "Even against weaker sides.
"When we don't concentrate we can easily drop points.
"The problem with Celtic is that they are very dependent on the scoring of Henrik Larsson.
"When he has been out injured the side has problems securing wins."
