The Bank of Montreal poll found that 73 per cent of those surveyed expect retailers to keep taking pennies — regardless of the circumstance or amount of their purchase.
And 59 per cent say small businesses should adjust their prices to benefit the consumer.
"Business owners are completely aware that they don't want to inconvenience customers; they want to maintain their relationships," said BMO's Joe Collura said Wednesday.
He added that the businesses that are "going to win the day" will be the ones who pass along the cost saving and convenience to their customers.
Retailers who decide to no longer accept pennies as part of cash payments will have to round up or down consumer purchases to the nearest five cents. However, electronic transactions, such as those on debit cards or credit cards, would still be registered in cents.
The BMO survey also found that 66 per cent of those polled currently pay for their daily purchases with a debit or credit card.
"A lot of business owners understand that folks are moving away from having to pull that penny out of their pocket, so to speak," said Collura, a small business area manager with BMO in Toronto.
"There is a large portion of Canadians that actually turn to cashless options as a way to purchase."
Consumers also seem to think that paying with less loose change will make the process go faster, with 67 per cent of those surveyed say they believe speed of service will increase without the penny.
The Royal Canadian Mint started collecting one-cent coins earlier this month for melting and recycling of the metal content, with some six billion pennies expected to be surrendered by Canadians over the next six years.
Finance Minister Jim Flaherty announced the surprise demise of the one-cent coin in last year's budget, saying the penny had become a nuisance.
While the Mint officially ended its distribution of one-cent coins to Canada's financial institutions, businesses can still accept the pieces as long as they choose.
Collura said that eliminating the penny will be done in a "customer friendly way" and the coins will go out of circulation as businesses take them to the bank.
"We're just going to see a different way of doing business as we move forward."
The online survey was conducted by market research firm Pollara between Feb 7-10 with a random sample of 1,400 adult Canadians.
Also on HuffPost