Despite sitting 10 points clear at the Scottish Premiership summit with six games remaining, boss Brendan Rodgers says Celtic "have a lot of work to do".
Wednesday's goalless draw with Dundee took the champions' lead at the top of the table into double figures.
But Rodgers' men were wasteful having enjoyed the majority of possession and goal-scoring opportunities.
"The finishing line is close, but we want to sprint over it, we don't want to just jog over it," Rodgers said.
"We want to get this league tied up as quickly as we can. But there's still a lot of work to do. Six games, still a lot to play for. We'll be better than what we were in the final third tonight, but lots of real positives - Craig Gordon coming back in, young Jack Hendry did well - it just wasn't to be."
Gordon, Celtic's goalkeeper, was playing for the first time since injuring a knee in late January, and pulled off a good early save to deny Simon Murray.
Although Dedryck Boyata's sliding tackle on Roarie Deacon almost sent the ball bobbling into the home net, Celtic were by far the dominant attacking force.
James Forrest and Scott Sinclair in the first half, then replacement Odsonne Edouard and former Dundee defender Hendry in the second, all went close to breaking the deadlock.
"We played well in terms of circulation of the ball," Rodgers told BBC Radio Scotland's Sportsound. "We could've been a bit more aggressive going into the final third both in our counter-pressing and our opportunities when we got in there.
"I thought the players' effort and attitude in the game was very good. Tonight we just lacked that little bit of quality in the final third. We've got good quality players but a mixture of us not making the final pass or not getting our shot away and them defending well meant we didn't score.
"When teams come here their game and their energy goes up an extra 10-15% so it was always going to be a real difficult game for us.
"I'm pleased with the desire in the team, we just have to get back to that better combination play in the final third. And I felt at times it was a little bit tired in our efforts on goal, and that's at the end of a really brutal season, a lot of games.
"But we kept a clean sheet; six games to go, 10 points in front, we'll take that."