Following the 1-0 home defeat by Arsenal in Sunday's north London derby, the former Celtic boss was asked about a pre-season interview where he said "usually in my second season I win things".
In response he said: "I'll correct myself - I don't usually win things, I always win things in my second year. Nothing's changed."
Former Australia boss Postecoglou - who also won silverware at South Melbourne and Brisbane Roar as well as in Japan with Yokohama F Marinos - takes his Spurs side to Coventry in the third round of the Carabao (League) Cup on Wednesday night (0500 Thursday AEST).
Spurs' last trophy came when they lifted the League Cup in 2008, and Postecoglou was again pressed on the comments.
"It is amazing, isn't it? I just stated a fact and it seems like am I supposed to just lie or just say it never happened?" Postecoglou said at a press conference.
"It is confusing to me that people are making a big deal out of something - surely I am supposed to answer something that is true?
"Like if I don't win in the second year this year, and I come out next year and say, 'well I always win in it'... well no, actually it is not true.
"But I have just said something that is true and it seems like it has upset a lot of people for some reason."
Postecoglou added: "Do you really think it's me sort of boasting?
"How am I supposed to answer something that is true? Is it to say, 'well, actually, it wasn't that important. They were easy competitions, and they don't mean anything'?
"If you have achieved something, aren't you supposed to say, 'yes I have and that's what I hope to do again'?
"I am not really sure why people misconstrue it as me trying to boast about something. I have answered a question which is true.
"That's always happened and my plan is for it to happen again this year - and if it doesn't happen, then I can't answer that question the same way next year, I can say 'mostly', and not 'always'."
Postecoglou is likely to utilise his squad against Coventry, who reached the semi-finals of last season's FA Cup, where the Championship side were beaten on penalties by Manchester United after fighting back from 3-0 down.
Youngsters Archie Gray, Lucas Bergvall and Mikey Moore could all be involved, while Ben Davies, Radu Dragusin, Djed Spence and Timo Werner should also feature.
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