The first minister said the Scottish government is looking at options on how the scheme can progress without damaging Scottish businesses, but if no alternative can be found, the proposals may not continue.
Scotland's DRS is due to begin in March 2024, with the earlier start date forcing ministers to seek an exemption from UK-wide legislation which aims to ensure there are no trade barriers between the four nations.
The UK government agreed the temporary exemption from the Internal Market Act, but insisted the Scottish scheme cannot include glass in order to match a similar initiative in England due to begin in 2025.
Under plans outlined for Scotland, shoppers would pay a 20p deposit every time they buy a drink in a can or bottle, with that money refunded to them when the empty containers are returned for recycling.
Yousaf said excluding glass could be at the "severe detriment" to Scottish brands such as Irn-Bru and Tennent's.
The issue has caused another constitutional row between the Scottish and UK governments, with Yousaf claiming the move seeks to "undermine" devolution.
Speaking during a visit to Falkirk on Wednesday, Yousaf said: "The choice that we are faced with is either to concede to the UK government's unreasonable demands as part of their attempt not just to torpedo the DRS, but frankly to undermine devolution. That would be to exclude glass, but to do so may well be at the severe detriment of businesses in Scotland."
He claimed it is an attempt by the Conservatives in London to "destroy" devolution in their final "12 to 18 months" in government, ahead of a general election expected next year.
Asked how the scheme could move forward without the exemption, Yousaf said: "We've got to give that consideration if we progress without glass and if it's going to harm Scottish business in that way, then yes, another choice is not to proceed with the scheme, which would be hugely disappointing given that the (Scottish) Parliament of course voted for the scheme and voted for these regulations."
Earlier today on BBC Radio's 'Good Morning Scotland' programme, Lorna Slater, the minister responsible for the deposit return scheme, said the Scottish Government needs to "quickly re-evaluate" whether the plans can go ahead.
She said: "We've hit a real roadblock with the UK government, at this very late hour, changing their minds and saying we can't have glass in the system when businesses all over Scotland have put in already the investment to having glass in the system.
"We now need to re-evaluate, talk to all the businesses in Scotland who have made this investment and figure out how we go forward from here."
Asked if the UK government's decision presents "insurmountable" problems for the scheme in Scotland, she conceded: "This is the question we need to work with Scottish businesses to find out: is it insurmountable? We have to rerun all the numbers very quickly, look at what investment has been made and see if we can move forward.
"A deposit return scheme is the right thing to do but Westminster really has thrown a spanner in the works and tried to sabotage the system and we are going to have to see if what they have left us is viable."
Slater added that the "UK government forcing us to take glass out of the scheme this late in the day is a challenge", as she accused the Tories at Westminster of U-turning on their plans for DRS.
