The midfielder secured a move to English Premier League outfit Stoke City on transfer deadline day to save him from dropping down to the Third Division with the Ibrox club.
But Klinsmann believes his agent should have secured a new club much sooner rather than leaving the player in limbo as he was training at Murray Park without taking part in matches.
He said: "It was a long stretch for him the last couple of weeks and months of figuring out where he would go.
"For me, it was not understandable how a player like him could be without a team for such a long period of time. The Rangers situation didn't happen yesterday. It happened three months ago.
"The agent should have done a quicker job to find a good club for him, not just a few days before the deadline."
With Edu gone, Ally McCoist has boosted his midfielder options by signing Australian midfielder Francesco Stella and the 21-year-old – who is still awaiting international clearance – has signed a one-year deal and can't wait to get started.
He said: "It's a great move for me to join such a big club. I knew of Craig Moore, Tony Vidmar and Kevin Muscat. I'm happy to be the latest Australian to come to Rangers.
"I had a few problems with Siena. I had another year of my contract to run, but we came to an agreement and I was a free player.
"There was an opportunity to come here on trial and I couldn't say no. So I was here for two weeks and then signed a deal last Friday. I was with Siena for about two and a half years. Initially, I signed as a youth player, but in the second year I moved into the first team squad."