The dramatic draw left the Socceroos second in Asian Group C behind runaway leaders Japan with four matches left and their fate in their own hands.
The top two go straight to the 2026 World Cup in North America.
But Australia are just a point ahead of Indonesia, Saudi Arabia, Bahrain and China, with all to play for.
Popovic’s side took the lead after just 38 seconds in Riffa through Kusini Yengi, only for Mahdi Abduljabbar to hit back in the 75th and 77th minutes to put Bahrain 2-1 ahead.
Portsmouth striker Yengi struck again in the 96th minute for what could be a vital point.
“Crazy game,” Popovic said after Tuesday’s qualifier, adding: “We showed a lot of character to come back and get an important point.”
Popovic has overseen a win and three draws since taking over from Graham Arnold, who quit as coach in September after a slow start to the third qualifying phase.
The Socceroos were held 0-0 at home by the Saudis last week.
“We would have liked to have won the game against Saudi or here tonight, which would have put us in a much better position,” said Popovic.
“But we’re second in the table — very different from where we were four games ago — and we have to look forward.
“Apart from Japan everyone is taking points off each other and tonight was evidence of that again.
“We put ourselves in a very good position at half time to win the match but missed a very good opportunity before their goal to go 2-0 up, and this is the story of the group.”
Australia next face crunch qualifiers home to Indonesia and away in China in March.
“We’ve got to make sure that March is a very good window for us,” Popovic added.
If Australia miss out on second in the group their World Cup hopes are still alive, as long as they finish third or fourth, which would put them into a further round of qualifying.
AFP