Searching for a new home following former side Rangers' relegation from the Scottish Premier League in financial meltdown, the American had to wait until the final hours of the summer transfer window before finally landing at Stoke City.
"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 could a player like him be without a team, basically, for such a long period of time," Klinsmann told reporters.
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"I think the agent should have done a little bit of a quicker job to find a good club for him, not just a few days before the deadline."
The agent, Lyle Yorks, also represents fellow USA international Clint Dempsey, bringing the forward to Tottenham late on deadline day.
Edu, a versatile American defender and midfielder, had completed a medical with time to spare when he agreed terms on a three-year deal with the Potters but had to wait for details of a work permit to be finalised before the official announcement was made on Friday. He joins countryman Geoff Cameron as new arrivals at the Britannia Stadium.
"It's been a hectic and a little bit of a stressful time for the players at the transfer period, but we are all thrilled that they all found clubs of a certain caliber," Klinsmann added of the pair's moves.
Fellow Americans Carlos Bocanegra and Alejandro Badoya also left Rangers after the Scottish giants filed for bankruptcy and moved to the Third Division as a Newco. The former completed a move to Racing Santander of Spain's second division, while Bedoya left Scotland for Helsingborgs.