Mr Obama said the outgoing commander-in-chief has shown a disregard for scientific evidence and public health advice during the crisis.
The former president also criticised the White House for failing to communicate effectively with the country at the onset of the outbreak.
His comments were broadcast as health officials reported 178,200 new coronavirus infections nationwide and deaths crept towards the 260,000 mark.
"This would have been hard for anyone," Mr Obama told Late Show host Stephen Colbert, without directly naming Mr Trump.
Some aspects of the pandemic response were not "rocket science", Mr Obama added, as he lashed out at the defeated incumbent’s “shambolic” handling of the crisis.
"We're not talking about inventing vaccines, which are now coming on board," he went on.
Mr Trump could have done better by "communicating effectively" and “respecting the science".
Throughout his unsuccessful re-election campaign, Mr Trump repeatedly refused to advise the American people to wear face coverings.
He belatedly did so in July under mounting pressure from public health chiefs.
By that stage, the virus was already spreading rapidly throughout the country, with thousands of people picking up the infection.
Throughout September, cases began to soar as Mr Trump launched a full-on assault at hanging onto the White House.
He crisscrossed the country to hold campaign rallies that were in some cases attended by thousands of people.
By October Mr Trump caught the disease and ended up in hospital, but still continued to flout public health guidelines upon his release.
Earlier this month, one of America's top infectious disease experts, Dr Anthony Fauci, said Mr Trump hadn't attended a coronavirus task force meeting for "months".
Speaking to Mr Colbert to promote his new best-selling memoir A Promised Land, Mr Obama also hit out at Republican lawmakers who gave oxygen to Mr Trump's so far baseless claims of voter fraud at the election.
"One of the big challenges that Joe Biden is going to have is to figure out how to puncture that information bubble that, not just Republican officials, but a sizable portion of voters are in right now,” he said.
Mr Obama also said president-elect Joe Biden and vice president-elect Kamala Harris's future administration would "pay attention" to the country and attempt to "do right by all people and not just some.”