Dimona won the shootout 23-22 after each side took 28 penalties.
Bachar, 44, won six Israeli Premier League titles between 2016 and 2023, with Hapoel Beersheb and Maccabi Haifa.
The announcement comes amid a call to boycott the Israeli team in world games by 12 countries.
Mac TA edges Netanya • Refaelov, Mac Haifa beat Hapoel in derby • Berkowitz grabs draw for Beitar vs Sakhnin
Puma made the decision to stop supporting Israel's national soccer squad because of financial reasons.
"We want to provide an opportunity for the people of Israel to unite around an event that embodies national pride and a triumph for the Blue and White," the initiative's organizer said.
Mac Haifa edges Hap Jerusalem • Mac TA handles Hadera • Beitar notches road win at Ashdod
In recent years, Israel has hosted European and global tournaments in lacrosse, flag football and athletics, and will soon add volleyball, water polo and baseball to the list.
The president of the Israeli Athletics Associationsaid Israel hosting so many tournaments has broken a glass ceiling in terms of Israel’s standing in the world, both politically and in sports.
With a loss, a draw and just one group game left, National Team must beat the Czechs and get help to advance.