Brendan Rodgers insists that he is greedy for more of his team, despite seeing them put six goals beyond Dundee in a polished exhibition.
Advancing through the penalty awarded by Arne Engels, Celtic added a second in the detention time of the first half through Adam Idah.
Daizen Maeda brought his account for the season to 18 with a double half before Engels added a fifth and sub Nicolas Kuhn concluded the score.
The champions now have 13 points ahead at the top of the table with only 13 remaining games and, while Rodgers was delighted with the exhibition, he told their players that they want them to deliver even more.
“I thought from minute one to the 93rd minute that we were outstanding in the game: our hunger and mentality,” he said.
'I said the other day that we have a different mentality from the defensive and that obviously creates the platform for our football tonight.
Jota and Maeda celebrate after the Japanese end scored the first goal of their double
Rodgers embraces Jota after a successful first game in Celtic Park for the Portuguese
It is 1-0 for Celtic since Arne Engels scores the first goal against Dundee from the point of view of the penalty
'Some of the goals were so good and only our general play was outstanding.
'I think Daizen has 18 goals, with a number of assists. Nicolas has 17 goals. I don't know how many assists, but it has a lot.
'Adam obtaining its goal, you see it now, it is moving differently and frees it a bit. He wants to really try a point and show that he is not 9 here constantly for Celtic.
'That has always been our goal. But obviously I am greedy and I want more. I want more players and I want to maintain our levels and keep improving.
'Because it's not just about every week and every month. It is every game that we want to improve and be the best we can '.
Even six goals ahead with remaining nine minutes, Celtic appetite for more goals did not decrease.
“The team was hungry.” Rodgers added. 'I think we knew when we played Dundee before we were well in the future. We scored three goals but, defensively, it was not very good.
'But tonight you see that we hunt the game in packages and obtained numbers around the ball, winning it and suffered the attacks. Some of our goals were a pleasure to see.
Adam Idah slides on his knees to celebrate after putting it 2-0 for Parkhead's side
The extreme Maeda scores Celtic's third goal on a night when the league leaders were tear
Maeda Wheels Away after scoring his second goal that Rodgers felt it was the best of the night
On a night when the standard of Celtic's objectives was remarkable, the second of Engels, the second of Maeda and Kuhn's Strike were all contenders for the best on exhibition.
When asked which one felt over the lot, Rodgers said: 'I think Daizen (second) was a great goal. Because? Because it starts right in the corner.
We are under pressure. Dundee are there, they want to press. We keep the calm, we connect the game, we take it out, we take it out of the other side. Arne's pass and then nobody would probably see Daizen scoring a goal like that.
'But what finish was. So, that was a great goal. As Nick was.
Rodgers is satisfied with the position that his side holds in the league, but will give nothing for granted.
“We cannot complain because I think that, until now, we have had an absolutely outstanding season,” he said.
'As you say, there are 13 games, 13 clear points, a big goal difference, which is always worth a point in itself.
Engels also got his second goal from the night, which did 5-0 against Dundee de Shellshocked
The Nicolas Kuhn substitute also entered the event, scoring to put the 6-0 for the champions
Rodgers was delighted with the exhibition, but says he is greedy for more of his players.
'I have always said that it is really about narrowing in the approach at this time of the season. Keep your hunger, keep your humility and keep thinking about performance. That was the message tonight.
The Chief of Duende, Tony Docherty, whose team crashed into the consecutive defeats of 6-0 after suffering the same score against Hearts last Saturday, said: 'It was difficult at the end.
'His pride will be detained and I want that case, but suddenly we do not become a bad team.
“We assume all the responsibility and we have to be more defensive, but we need to return to the horse now.”