Italy were beaten 2-0 by the Netherlands in their quarter-final on Saturday having impressed in their first appearance at the finals since 1999.
The 'Azzurre' finished above Australia and Brazil in the group stage and beat China in the round of 16.
Bertolini said the performance of her team, who have captured the attention of Italian fans in an unprecedented fashion, was "exceptional", but action was needed to ensure continued progress.
Italy's top Serie A clubs have recently begun to take the women's game more seriously, but legislation enforces a salary cap of around 30,000 euros ($34,104) on players who legally and contractually have amateur status.
"We must never forget the Italian players here have competed against fully professional players while our girls are amateurs. Thanks to our team spirit, we were able to reduce the gap but the most important thing now is that the clubs and governing classes allow them to work in the same conditions as their foreign counterparts," she told a post-match news conference.
"The big clubs are already doing a great deal. They have started this process two years ago in order to change the women’s game. But it will also require political decisions," she added.
"The political classes will need to make significant decisions in regards to women’s sport, and more specifically women’s football," she added.
The Italy coach contrasted the sportsmanship and "positive values" of the women's game with some of the controversies that have surrounded men's football in Italy and said it was the way her players approached the game that had won over the Italian public.
"They need to be proud of themselves. The way they played and approached matches and their passion, they’ve shown people back home that football can be a sport where you have enjoyment, helping one another, unity and all these values. I think that’s why the public have fallen in love with this team," she said.
The Italy players were in tears after the loss and Bertolini said she had also been overcome by her team's exit from the tournament but she felt no bitterness in defeat.
"We all cried. When we huddled together there were more tears. When you really commit a great deal to what you do then naturally you are emotional and upset," she said.
"The girls are all in tears because they had this dream and the dream is over. But this is a starting point and we need to push on from this with a lot more confidence."
($1 = 0.8797 euros)
(Reporting by Simon Evans; Editing by Toby Davis)
