Swiss coach Grings proud of squad's overall performance in Women's World Cup
Switzerland also exited the tournament at the last 16 stage in 2015 but had advanced this time around as group winners finishing ahead of Norway Norway and co-hosts New Zealand.
"There is nothing that any of my players did wrong. They did everything right. They played a really, really good tournament," the German said.
"I think that my team has invested everything and I'm very, very proud of them. That group has shown that we are on the right way."
Grings acknowledged the professional game in Switzerland needs to be stronger if they are to make a bigger splash on the world stage, as she has players who miss training because of secondary jobs.
"These are topics that we have to discuss about," Grings said. "But of course, we can also not change from zero to 100 that quickly, but we have to start progressing towards those changes.
"And what's also important is that the players, no matter where they play, whether they play in Switzerland or outside of Switzerland, that they actually get to play."
Grings made 96 appearances as a player for two-time World Cup champions Germany. Spain were not on the global women's soccer radar during her playing days, showing how fast some nations are making progress.
"There are many nations who are catching up or not even catching up but who are just basically continuing on their path and are just progressing," Grings added.
"Unfortunately, we're on the receiving end of that today. But we have seen that over the last year that it was a constant development, and I think that that's one of the reasons why football is so successful at the moment."