Some internet firms are "not cooperative" and "won't help" intelligence agencies, he said during an event at the Digital Catapult centre this week.
"You need an agreement [to access data] with the internet service providers, some of whom are cooperative," he said.
"If you provide a warrant to Google, Google will provide the material, albeit rather slowly as it's based in the US and they require Department of Justice processing. Other companies won't help," Omand added.
Google's publicly available transparency data shows the company received 708 requests for data from the UK between 2009 and 2013 and approved 64 percent of them, on average. More recent data was not available.
Google has strongly denied intelligence agencies have access to its servers, either directly or through back-door arrangements. The search giant said it provides data "only in accordance with the law", and only when its lawyers are satisfied requests are not too broad and follow the correct process.
Omand's comments came in the same week as an official review called for the UK government to overhaul existing online surveillance laws.
He said the government should work to get any new laws on the statute book by the end of 2016, as this is when existing "emergency" legislation on data retention expires.
Omand said the main challenge facing the internet today is public confidence. Although he acknowledged the Snowden leaks had undermined public trust in online privacy, Omand said revelations "about the monetisation of personal data by companies" had also played a major role.
"We've sold our souls to the internet. Who's in charge No one," he said.
But the way to improve low public confidence is not implementing strong encryption everywhere, according to Omand.
Last month Google, Apple and other big tech firms signed a letter to the Obama administration arguing "strong encryption is the cornerstone" of the modern information economy and should not be undermined or weakened by governments.
However Omand said extensive encryption would "screw up law enforcement and make the internet a 'Wild West' where the most terrible things can happen".
He said there should not be government back doors into encrypted online services, but equally "we can't be in a position where the internet is a law-free spacethat's not a position that's very responsible".
However Omand was keen to draw a distinction between mass surveillance and unlimited access to online data by intelligence agencies, which he said was "physically unfeasible", and "bulk access" to data.
Bulk access is necessary when, for example, the police service have identified one suspect in a paedophile ring and need to find out who they had been in contact with, which websites they visited and images they downloaded, he argued.
"That's when you need, as it were, the bulk access. You've got to get access to that information, some of which is historic. It's in the discovery of new leads that the bulk access to communications data is so crucial," he added.
However Omand admitted: "You really need to have a legal framework. As citizens we need to know how the law impacts upon us, and we have to be very confident that what is being done is in accordance with the law."
Omand currently serves as a commissioner for the Global Commission on Internet Governance and is a visiting professor at King's College London. He started his career at GCHQ and was director from 1996 to 1997. He served in senior positions at the Home Office, Ministry of Defence and Cabinet Office before retiring in 2005.