The new coach seemed set to triumph in his fourth match at the helm of the two-time European Cup winners thanks to a first-half brace from Igor Jesus, after Cedric Bakambu sent the Spanish side ahead.
However Antony popped up in the box to slot home in the 85th minute and claim Betis a share of the spoils.
Postecoglou, who won the Europa League last season with Tottenham before being sacked little over a fortnight later, is aiming to end Forest’s wait since 1990 for a major trophy.
“It’s a difficult place to come, difficult conditions, people don’t realise the humidity out there, how energy-sapping it is, even the pitch,” Postecoglou said. “I thought our football was outstanding at times in the first half. The thing I could fault is we didn’t put the game to bed.”
Forest’s coach dropped target man Chris Wood to the bench in favour of Jesus, and the striker signed this summer from Botafogo delivered for the Australian.
Betis’ key man was former Manchester United winger Antony, and he helped create the opening goal.
Hosting the game at the Cartuja stadium in Seville while their Benito Villamarin home undergoes renovation, Betis took the lead in the 15th minute through Bakambu.
Antony floated inside from the right and fed the DR Congo international, who turned and drilled into the top corner at the near post.
Forest levelled swiftly through Brazilian striker Jesus, who tapped home from close range after Morgan Gibbs-White’s low pass cut through the defence to find him.
Jesus had his second just five minutes later, heading in from a corner as Betis left him in space.
Callum Hudson-Odoi almost grabbed a third but hit the post with the goal gaping. It came to cost Forest. (AFP)
