The left-back made just 15 appearances for Manchester United last season but was not selected by van Gaal for Holland's World Cup squad.
Buttner is disappointed that van Gaal, who will start work at Old Trafford next week, did not give him an opportunity to play for the national team during his two years at United.
The 25-year-old has questioned the use of Dirk Kuyt as a wing-back during the World Cup in Brazil and believes he could have made a positive contribution during the penalty shoot-out defeat by Argentina in the semi-final.
However, after completing a move to Russian side Dinamo, Buttner feels he will be in a stronger position to press his international claims under van Gaal’s successor Guus Hiddink.
"I have been unfairly ignored," Buttner is quoted by The Sun. "I played for Manchester United in the Champions League against Arjen Robben and I was man of the match.
"I am disappointed in van Gaal for not giving me a chance. Kuyt? I don't want to talk about other players.
"But when I see how the left-back position was filled against Argentina, I know that I could have played there.
"Few people can say they played for Manchester United's first team.
"Dinamo showed interest in me while I was still playing for United. And I could have joined clubs in Germany, France, Italy or Turkey, but Dinamo gave me the best feeling.
"I now want to break into the Dutch side through playing for Dinamo. The incoming coach, Guus Hiddink, knows Russian football better than anyone."