The Argentina international made the switch to France, having missed United's pre-season tour of the USA, bringing an end to a disappointing one-season spell at Old Trafford.
Barcelona forward Pedro is reportedly United's top target, and van Gaal admits that while the "problem" of selling Di Maria has been solved, his exit has left a void in his squad.
"Di Maria, we have solved that problem but it is for us a big loss," he said.
"When I say I want more attackers with speed and creativity, Di Maria is one of those players so we have to look for those kinds of players."
Di Maria managed just three goals in 27 Premier League appearances last term, and Van Gaal believes that his exit was the best for all parties.
"He started very well," he added. "That is not the problem.
"He had a very good start. He knows the answer better than I know but it happens and then there is only one solution, what he has done.
"Of course they [players from abroad] have to have the talent to cope with the English rhythm and that is difficult to find.
"That is mostly also why players are not having success in this competition because of the rhythm of the game.
"The English culture is another culture from the Latin culture. You never know. As a manager you never know."
