A 2-1 loss at Aston Villa in the fourth round of the FA Cup on Sunday came on the heels of an exit from the English League Cup semi-finals after a 4-0 second-leg thrashing at Liverpool on Thursday.
With Tottenham languishing in 14th place in the Premier League, the team's only chance of a first piece of major silverware since 2008 lies in winning the Europa League. Spurs have advanced to the last 16 of the second-tier European competition.
In September, Postecoglou put pressure on himself by saying in an interview: "I don't usually win things, I always win things in my second year (with a team). Nothing's changed."
He was referring to spells at Australian clubs South Melbourne and Brisbane Roar, Japanese side Yokohama F. Marinos, Scottish giants Celtic and also with the Australia's national team, who won the Asian Cup in his second year as coach.
Postecoglou has only a few months left of his second campaign at Tottenham, where he started so promisingly - the team was undefeated and top of the Premier League after 10 games of his first season - but has imploded, leaving question marks over the Australian's style of play.
Tottenham has been ravaged by injuries this season as the games came thick and fast in a number of competitions, and at least now has gaps in the schedule for more rest before recovering key players like Cristian Romero, Dominic Solanke and Micky van der Ven.
Postecoglou is happy for people to say what they want about him, but insists no other team could have coped with the injuries he has had to deal with over the last few months.
"It can't be that people think that's an excuse," he said. "That's just not anywhere near close to objective analysis. That's just agenda driven stuff.
"If it's to get rid of me that's fine. Good on ya. Go for it a million times. But in terms of this group of players, what they've given over the past two and half months has been outstanding, it's a credit to them, I can't speak highly enough of them."
He added: "They will get some opportunity to recover now, we'll get some players back over the next couple of weeks and we'll look forward to resetting and finishing the season strongly."
Postecoglou will hope for more goals from Mathys Tel, a 19-year-old French forward who joined on the last day of the winter transfer window and scored a late strike against Villa to set up a tense finale.
Ultimately, Tottenham was undone by a big error from goalkeeper Antonin Kinsky, who let a shot from Jacob Ramsey squirm through his grasp after just 57 seconds. Morgan Rogers added a second for Villa in the 64th.
"Wasn't a great start — it's the last thing you want," Postecoglou said. "That gave them some momentum for the first 45 minutes and we struggled to get some control."
- with PA
