A massive clean-up operation has begun after the storm left 84 dead and flattened homes, uprooted trees and left cities without power.
India's Prime Minister Narendra Modi has arrived in West Bengal state to conduct an aerial survey.
Authorities in both countries had evacuated millions of people before the storm struck.
Covid-19 and social-distancing measures made mass evacuations more difficult, with shelters unable to be used to full capacity.
Officials also said people were afraid and reluctant to move to shelters for fear of contracting the virus.
The cyclone arrived with winds gusting up to 185km/h (115mph) and waves as high as 15ft.
It is the first super cyclone to form in the Bay of Bengal since 1999. Though its winds had weakened by the time it struck, it was still classified as a very severe cyclone.
Three districts in India's West Bengal - South and North 24 Parganas and East Midnapore - were very badly hit.
In Bangladesh, there are reports of tens of thousands of homes damaged or destroyed and many villages submerged by storm surges in low-lying coastal areas like Khulna and Satkhira.
The affected areas include the Sunderbans, mangroves spread over an area of more than 10,000 square kilometres that spans both India and Bangladesh - the swampy islands are home to more than four million of the world's poorest people.
Those in the Sunderbans say it is too early to estimate casualties in the area, which is now cut-off from the mainland by the storm.
"There are houses which have collapsed and people could be trapped in them but we don't know yet," Debabrat Halder, who runs an NGO in one of the villages, told the BBC.
He recalls cyclone Bulbul in November 2019, which was followed by a huge incidence of fever, diarrhoea and flu, and is afraid that that the same may happen again.
And worse, he adds, is that the flooding from contaminated sea water, has likely destroyed the soil.
"Nothing will grow in this soil," he says, adding that it will likely take years to convert it into fertile land again.
Kolkata, the capital of West Bengal, and one of India's biggest cities has been devastated. Its roads are flooded and the city was without power for more than 14 hours.
The state's chief minister, Mamata Banerjee, said the devastation in Kolkata was "a bigger disaster than Covid-19".
But assessment of the damage is being hampered by blocked roads and flooding in all these areas.