An entertaining game at the Amsterdam Arena was settled in the visitors' favour by a double from Carlos Vela on his return to international football after a three-and-a-half-year absence and an effort from Javier Hernandez.
A fierce long-range volley from Wesley Sneijder and Daley Blind's deflected strike were rendered insufficient by the hosts' sloppy play at the back.
Bayern Munich winger Robben was highly critical of the Netherlands' performance, which marked the second time that Guus Hiddink has lost four of his first five games as coach after doing the same during his first stint in charge in 1995.
"We should not point the finger at each other," Robben told SBS6. "But we have to speak to each other about the errors that were made.
"We have no security or stability at the back and we fall into repetition.
"We get three against three [in attack], which means we had to make the right play. We have had those opportunities. The story has another side: we need to make more goals."
Hiddink has suggested that he will resign if Netherlands do not beat Latvia in Sunday's Euro 2016 qualifier, however, Robben would not be drawn on the team's opinion of their coach.
When asked if the team is behind Hiddink he replied: "I think that's a stupid question."
