Klose, Germany's all-time leading goalscorer with 71 goals, left Bayern Munich in 2011 after struggling to satisfy the Dutchman.
The 36-year-old played 60 games while Van Gaal was in charge of Bayern, but scored only 12 goals.
"It was a tough time, particularly working with Van Gaal," Klose told Germany's Die Zeit newspaper.
"I didn't feel free. It was very difficult for me to fulfil his expectations. He was asking me to make runs I just couldn't see.
"I gave it all I could, but sometimes it just wasn't enough."
Had it not been for the backing of the fans and the faith shown in him by Germany coach Joachim Low, Klose says he may not have emerged from the two years he spent under Van Gaal the way he did.
Klose has since gone on to score 41 goals in 101 games for Lazio, and broken Gerd Muller's goalscoring record for his country on his way to winning the World Cup last month.
He also became the all-time World Cup record scorer by taking his career tally to 16 goals at his fourth tournament.
"The support from the fans was always important for me," Klose said. "We as footballers are meant to excite the fans, but for me it worked in the other direction. Maybe that is why I was able to play without any worries."