Both the men's and women's 4x100m quartets failed to reach their finals on Saturday as baton handling errors cost them dear in the heats.
And, despite a record 19-medal haul in Barcelona, the Dutchman was damning in his criticism of his relay flops.
"The women were a disgrace and the men were not much better," he said.
Leading their first-round run going into the final leg, thanks to strong runs from Leon Baptiste, Craig Pickering and Marlon Devonish, disaster struck for Britain's men when Mark Lewis-Francis failed to collect the baton cleanly from Devonish.
Britain, who had been tipped for medal glory, eventually finished fifth in a time of 39.49 seconds as Lewis-Francis, who won silver in the 100m, accepted the blame for his team's early exit.
"This is my fault, I've let the guys down," an emotional Lewis-Francis told the BBC.
On the same day, Joice Maduaka, Montell Douglas, Hayley Jones and Laura Turner also saw their final qualification hopes thwarted by dreadful handovers.
Although not expected to get on the podium, their sixth-place finish in their heat in a time of 44.09sec was considered a lacklustre effort.
The performances brought back memories of other miserable major championship displays by British sprinters - there were dropped batons by British sprinters at the Olympics in Atlanta (1996) and Sydney (2000), as well as the World Championships in Edmonton (2001), along with a disqualification at the last Olympics in Beijing in 2008.
People really need to have serious questions asked of them - especially the "specialist" relay coach
Van Commenee, meanwhile, stated that the European Championships had been "mostly positive" for his team as the London 2012 Olympics draws closer into focus.
"I've seen quite a number of athletes stepping up a level, which is encouraging for the next two years," said the 52-year-old, who was appointed to the UKA hot seat in 2008 following Britain's disappointing showing at the Beijing Games.
Van Commenee claimed he would have been "embarrassed" not to achieve UK Sport's target of 10 to 15 medals in the Catalan capital and Britain picked up 19 in Barcelona.
Van Commenee encouraged by GB progress
Aside from the relay disappointments, he immediately identified other areas of weakness in the British team.
"There is a lot of work to be done," he added. "We have too many athletes at home with injuries. That needs to be addressed. We don't have enough athletes across the events, especially the field events, especially the women."