Coulson, who went on to head Prime Minister David Cameron's communications team at 10 Downing St, was in charge because the editor at the time, Rebekah Brooks, was on holiday in Dubai.
The court has heard evidence that the paper's private investigator, Glenn Mulcaire, who was paid 105,000 a year for his services, was given the job of illegally accessing the schoolgirl's phone.
Asked by Langdale if he was involved in, or aware of, the Dowler hacking by individuals on his newspaper, Coulson replied, "No I was not."
He told the jury he regarded the story of Milly apparently applying for a job in a Midlands factory as "unremarkable", and said it did not occur to him that any detail had been obtained by someone inside the News of the World illegally accessing the murdered schoolgirl's voicemail.
"I may have concluded that it came from sources, maybe police sources," he told the court.
Coulson said "catching criminals" was part of the News of the World "DNA" and told the court this involved working closely with the police.
Although this relationship was not "without tensions", he claimed there was no attempt by the paper "to interfere in police investigations".
Asked hypothetically how he would have felt if he had known the newspaper was involved in phone hacking, he said he would have been "very concerned".
"I think my instinctive concern would be that this was interference in a police investigation."
The first edition of the News of the World on April 14, 2002 referred to material taken from voicemails on Milly's phone.
The voicemail references did not appear in later editions of the newspaper.
The jury has heard that public outrage over the discovery of the Dowler hacking nine years later led Rupert Murdoch to close the News of the World in 2011.
Coulson, looking back on the story of April 2002 that contained the Dowler voicemail, told the court that the changes made to the positioning of the story inside the News of the World between the first and third editions were essentially cosmetic, because he wanted more "glamorous" content moved closer to the front of the paper.
Coulson said the decision to send eight reporters and photographers to the factory where they, wrongly, believed Milly would be found, was made by the newsdesk, not by him.
Coulson, 46, was giving evidence for the second day in his defence.
He told the court he could not remember conversations with Brooks involving any discussion about Milly Dowler.
Coulson is one of seven defendants in the trial. All have denied the charges against them.
The trial continues.
- Independent