The Gers kicked off their Europa League group stage campaign with a slender win over Real Betis, but on Thursday evening failed to follow it up.
Interim boss Steven Davis could not inspire Rangers to a win in Cyprus as they slipped to a 2-1 defeat, having been 2-0 down at one stage.
Thompson believes that Aris Limassol are far from a top European side and did not have to pull up any trees to beat Rangers.
He thinks that the Rangers players, who have struggled this season, again turned in a performance which was not acceptable.
“Aris Limassol aren’t a top European side. They didn’t have to do too much to win against a very poor Rangers team”, Thompson told BBC Sportsound.
“It’s not good enough, plain and simple. It’s a team devoid of confidence.
“To play for Rangers it takes leaders, big characters, players that roll their sleeves up and lead from the front.
“Not one of those players took that responsibility. They looked to each other for help. Too many players way below par with their performances.
“They needed a reaction. These players have again fallen short of the acceptable standards at Rangers.”
Rangers will now have to return their focus to the domestic stage with a clash against St Mirren on the agenda for the weekend.
