Baseball/softball, karate, skateboarding, sports climbing and surfing have been recommended by the organisers of the Tokyo Olympics for inclusion at the 2020 Games.
Under the proposal, a total of 18 new medal events, nine each for men and women, would be contested by an extra 474 athletes at the Games.
"I don't believe we could have done more to get our message across to both the Tokyo 2020 Games hosts and the IOC how squash could bring something special as an addition to the Programme," WSF President Narayana Ramachandran said.
"I know I speak on behalf of the millions of squash players around the world for whom the opportunity of seeing their sport participate in the Olympics has been an absolute priority. Like me, they will be heartbroken.
"However, this is not the end for squash."
Olympic host cities can now hand-pick sports they want to see contested at the Games, although the final decision rests with the International Olympic Committee, which will vote on the 2020 recommendations next August.
Bowling, squash and wushu had also been short-listed for inclusion in Tokyo but were left off the final recommended list.
"This package of events represents both traditional and emerging, youth-focused events, all of which are popular both in Japan and internationally," Tokyo organisers said in a statement.
"They will serve as a driving force to further promote the Olympic Movement and its values, with a focus on youth appeal, and will add value to the Games by engaging the Japanese population and new audiences worldwide, reflecting the Tokyo 2020 Games vision."
Organisers wanted sports already popular with Japanese youth so new venues would not need to be built and add to ballooning costs.
Baseball and softball, united under the World Baseball Softball Confederation (WBSC), were previously on the Olympic programme but were dropped after Asia last hosted the Summer Games, in Beijing in 2008.
Karate has never been contested at the Olympics. Judo, another martial art founded in Japan, first joined in 1964, when Tokyo last hosted the Summer Games, and has been included on every programme since 1972.