Jota and Kyogio Furuhashi both scored twice as Celtic won 4-2 against Dundee at Dens Park.
They remain four points behind leaders Rangers who beat Ross County 4-2.
Celtic's victory was marred by fan behaviour with some Celtic fans disrupting both a Remembrance Sunday silence and kick-off.
Australian Postecoglou called for fans to show more respect in connection with both incidents.
The silence - to commemorate the contribution of British and Commonwealth service people in the two world wars and later conflicts - was not observed by a small section from the start.
Referee Alan Muir appeared to call an early halt after some away fans started singing a song about Aidan McAnespie, who was shot dead at a British Army checkpoint in County Tyrone in 1988.
Postecoglou said: "You would have to ask the individuals why they felt the need to do that.
"My view is pretty simple, that we treat these things with respect and dignity and that's what we try to do.
"We certainly did and I think the majority of the fans did because that's the kind of football club we are."
The start was then delayed after Celtic supporters threw dozens of tennis balls on the pitch in a protest over claims that the club is considering appointing Police Scotland assistant chief constable Bernard Higgins in a senior security role. A banner directed at acting chief executive Michael Nicholson read: "Fans or Higgins? Ball's in your court, Nicholson."
Several of Postecoglou's players helped clear the balls off the pitch and the delay did them little harm with the visitors going two ahead inside 20 minutes.
When asked about the tennis ball protest, Postecoglou said: "My view on all those kind of things is that we live in a society where people are allowed to express themselves.
"It's not necessarily a bad thing but I'd rather protect the sanctity of that 90 minutes because I know how precious it is and if we want to be a successful team we need everyone united for that."
For Celtic Kyogo Furuhashi and Jota both scored early in each half with each brace met by a single Dundee goal, from Danny Mullen and Lee Ashcroft respectively.
"We were disappointed to concede two goals," said Postecoglou. We just got a bit sloppy. But we played some excellent football at times, controlled the game and played it on our terms."
Rangers survived an early scare when bottom side Ross County led through Joseph Hungbo after only five minutes. County. also scored late through Jordan White.
But in between Rangers got four: Joe Aribo, Ryan Kent, Juninho Bacuna scored and James Tavernier's cross was deflected into his own goal by County defender Alex Iacovitti.
12°C