Celtic manager Ange Postecoglou says the Scottish Premiership title is not an "insurmountable challenge" after his side's troubled start continued with a draw against Dundee United.
A terrific Ian Harkes header quickly cancelled out Liel Abada's opener to leave Celtic sixth, six points behind leaders Rangers.
The hosts hit the woodwork three times and Albian Ajeti astonishingly missed an open goal from three yards, while United had a strong penalty claim rejected when Nicky Clark was felled.
"It's a weird league," said Postecoglou. "You call things early here, don't you? It's quite remarkable that seven games in people are calling the title already.
"I'm not pulling up stumps after seven games just because other people seem to think there is some sort of insurmountable challenge out there for us.
"I know people are wanting to push me on some kind of edge of the ledge somewhere. It's just not going to happen."
Thomas Courts' youthful United showed impressive composure and withstood a late barrage in a breathless contest to collect their first point at Celtic Park in eight years.
They are a point above Celtic in fifth, while Postecoglou's already lengthy injury list claimed another victim in Josip Juranovic.
While Celtic have made their worst start to a league season in 23 years, they had been flawless at home with three straight wins in sharp contrast to three away defeats.
United halted that record and seized on Celtic's sloppiness. The hosts Celtic built early momentum - Juranovic had a shot batted away by keeper Benjamin Siegrist and Ajeti headed too high - before their wingers combined for the breakthrough. Jota jinked down the left and cut in to swing over a cross met with a thumping Abada header at the back post.
The setback galvanised United and they were level within two minutes. Finnish winger Ilmari Niskanen outmuscled Anthony Ralston down the left and his whipped delivery was brilliantly converted by Harkes with a diving header.
Both sides had reason to feel aggrieved not have a half-time lead. United, whose high press unsettled Celtic's defence throughout, were bemused by referee Kevin Clancy's decision not to award a penalty when Cameron Carter-Vickers sent Clark sprawling.
At the other end, Ajeti inexplicably blazed over an unguarded net and David Turnbull sent a 20-yard strike against the bar. Ajeti would be guilty of another glaring miss late in the second half, heading wide from six yards.
Postecoglou's men piled on the pressure after the break, but lacked conviction in the final third.
Jota looked their best hope of a winner, and almost got it with a dipping drive off the bar in the final few minutes. Tom Rogic also shook the frame of the goal with a header from Jota's knockdown as Celtic's late rally fell short.
United, though, defended diligently and remained a danger on the counter-attack. Niskanen was inches away from finding the far corner of the net with a curling strike, and the the visitors could have snatched a dramatic victory when substitute Louis Appere had a near-post drive saved by Joe Hart.
It then took a superb Carl Starfelt tackle to halt Appere in a two-on-one breakaway as the end-to-end action continued until the final seconds.
Man of the match - Ian Harkes
What did we learn?
Celtic can't get some of their key men back quickly enough. The leadership of Callum McGregor and finishing prowess of Kyogo Furuhashi were badly missed in a haphazard display.
Ajeti again failed to convince up front. The striker will never offer the movement of Kyogo, but should have converted at least one of the glaring opportunities presented to him.
United, to a man, were superb. With a young side featuring 16-year-old Kerr Smith at centre-back, Thomas Courts' men caused the hosts all sorts of problems.
Having now beaten Rangers and held Celtic this season, and a derby win over Dundee thrown in for good measure, Courts has the Tannadice men handily placed in fifth.
What did they say?
Celtic manager Ange Postecoglou: "Obviously disappointed with the outcome but in terms of our approach I think it's exactly what our supporters want to see.
"We created a lot of chances, we just didn't take them. Sometimes football goes that way. On another day we score four or five."
Dundee Utd head coach Thomas Courts: "It [the penalty claim] was very legitimate. We watched it back at half-time and it was bitterly disappointing.
"This was a big ask for my players - three games in seven days including the emotion of a Dundee derby - but they were outstanding. I feel really proud of them."
What's next?
Celtic have a daunting assignment against in-form Germans Bayer Leverkusen in the Europa League group stage on Thursday (20:00 BST), before a Premiership trip to Aberdeen on Sunday (12:00).
United look to make it four league games unbeaten when they host Ross County on Saturday (15:00).