Martin O'Neill refuses to concede the Scottish title to Rangers despite his Celtic side slipping eight points behind their arch rivals.
O'Neill suffered at Dens Park but says the title race is not over
Celtic still have two matches in hand after Sunday's 1-1 draw at Dens Park, although those are both away from home, against Hearts and Motherwell.
And there is still one more Old Firm derby to come before the end of the season.
O'Neill said: "Overall, we did fine and we are far from finished.
"I still expect points to be lost in the championship race. Dundee is a difficult place to come to.
"We tried to get forward in the second half and left a number of gaps, which Dundee almost exploited.
"We got everyone in Dundee's penalty box and they broke on us with five men to one.
"I'm not sure that is the most sensible attitude to take. But, at the end of it all, we have been positive and tried to do the right thing.
The game was definitely there for the winning today
"We still have to go to Ibrox, so it is still within our reach. We still have to win all our games, which is a big task, but we are there."
O'Neill dismissed suggestions that his players had one eye on the Uefa Cup semi-final first leg against Boavista at Celtic Park.
O'Neill is confident that goalkeeper Rob Douglas and defender Joos Valgaeren, both missing against Dundee, will be fit for Thursday.
He will also assess the fitness of wing-back Didier Agathe, who has been out injured since 8 March, ahead of Monday's under-21 game against Livingston.
O'Neill said: "Rob Douglas will have a better chance of playing on Thursday because he missed out today.
"I hope that is the case and that is the same for Joos Valgaeren and Didier Agathe."
Alan Thompson gave Celtic an early lead at Dens Park, but former Celtic striker Mark Burchill equalised before Dundee missed several chances to win the game.
Dundee had been inspired with the thought that victory would ensure a place in the top six before the Scottish Premier League splits in two next weekend.
They have edged one point clear of Hibernian with one game remaining.
BBC Scotland man of the match Lee Mair said: "The game was definitely there for the winning today with the chances we had.
"I can't remember Julian Speroni having any saves to make apart from one in the first half from John Hartson, but Javier Sanchez Broto was brilliant."