He said the Central Bureau of Investigation (CBI) had also stated it in its "closure report" filed before a special trial court in Ghaziabad.
"The Allahabad High Court has, I believe, given them benefit of doubt which is precisely what we had said in our closure report. There was insufficient evidence to prosecute the Talwars hence we had filed the closure report," he told PTI.
The investigation in the case was almost complete when Singh became the CBI chief to head it between 2010 and 2012.
"The investigation was almost complete when I took over and I had to take a decision whether to file a charge sheet or a closure report," he said.
Singh said that there were several constraints before the CBI when it took over the investigation, and the most crucial one was the crime scene which was severely compromised after the Uttar Pradesh Police's initial probe.
Aarushi was found dead inside her room in the Talwars' Noida residence with her throat slit in May 2008. The suspicion initially fell on 45-year-old domestic help Hemraj, who at the time was missing. But his body was recovered from the terrace of the house a day later.
As the Uttar Pradesh Police drew flak over shoddy investigation into the case which was making national headlines, the then chief minister Mayawati recommended a probe by the CBI.
The case was handed over to the CBI on June 1.
The agency had filed its closure report in the Ghaziabad court on December 29, 2010.