Spurs regrouped impressively from Hugo Ekitike's fine sixth-minute opener for the visitors in their last-eight first-leg tie and forced a leveller after 26 minutes through an exquisite Pedro Porro back-heel.
It gave Tottenham a platform and they looked back to their best after the break during wave after wave of attacks as Lucas Bergvall and Rodrigo Bentancur hit the crossbar, while Son Heung-min and James Maddison were denied by excellent saves from Frankfurt back-up goalkeeper Kaua Santos during four dazzling second-half minutes.
Postecoglou rolled the dice late on and watched Brennan Johnson fire over before Micky van de Ven sent a close-range header onto his own foot which allowed Kaua to tip over and leave the tie finely poised ahead of next week's second leg at Deutsche Bank Park.
"I'm resigned to the fact that the football gods have got their eyes elsewhere this year. They're obviously busy with other clubs and other managers so whatever we get we're going to have to do it without them this year," Postecoglou smiled, in reference to Spurs' hefty injury list in the winter.
"If we can repeat that (performance) next week, and there's no reason we can't, we'll give ourselves a good chance.
"I really felt like we overwhelmed them with our football, with our running and with our press. It wasn't just the chances we created, but the chances we almost created.
"It's going to be that sort of season. Nothing is going to come to us easy. We're going to have to go there and fight now to get what I thought we deserved tonight and that's what we'll try to do."
Even though Spurs face an uphill task next week in Germany, Frankfurt's recent form at home has been mixed, with three defeats in March.
Tottenham's own inconsistency has been their Achilles heel this term but Postecoglou did take encouragement from this display.
He added: "A little bit frustrated by the result obviously, but I thought the performance in general was really good from the boys.
"We conceded early which was not ideal and it was a fair strike by the lad, but I thought our response to that was really good.
"We stayed in control, we scored a good equaliser and we made them work hard in the first half so we knew in the second half, with our ability to break teams open, we would put them under pressure.
"It is exactly what happened and the boys did everything right. I couldn't ask for anything more from them.
"On any other night we would have a comfortable victory. If we can perform like that over there, and there is no reason why we can't, then we still give ourselves a good chance."
