Vicario fractured his ankle during Saturday's remarkable 4-0 win at Manchester City and will not play again until the new year.
The Italy international has been a virtual ever-present since he signed in the summer of 2023 and featured in every Premier League fixture under Postecoglou, but the Australian coach will have to turn to back-up Fraser Forster for the foreseeable future.
Postecoglou said: "I guess a bit of a shock first of all because we saw he picked up an injury during the game and he was sore at half-time, but there was no doubt about him continuing.
"Post-game, again he was sore but you go, 'he's played 60 minutes, we'll tape him up and go again'.
"Externally now people realise it is testament to him as a person because he's as tough as nails and the fact he played 60 minutes with a fractured ankle is quite outstanding.
"Once the shock wears off, you have to process he'll be missing for a while but knowing him, he'll push the limits of how long that is and knowing him you'll get daily updates on his Instagram.
"It's a blow but we've dealt with setbacks before and we'll deal with this one."
While Postecoglou was reluctant to put a timescale on Vicario's recovery ahead of Thursday's Europa League home tie with Roma, he acknowledges it would be "months" out rather than weeks.
The Australian offered his backing to 36-year-old Forster, who has made three appearances this season, and revealed the club would not look at the free-agent market.
"We're happy with what we've got," he said. "I don't think us signing a free agent now is going to help us. This injury doesn't change any plans for (the transfer window in) January."
15°C