He also urged retailers to avoid putting up prices "at all costs".
But in a statement to Holyrood, Mr Swinney said the strike could have a knock-on "impact" on BP's Kinneil plant, which controls the Forties pipeline system.
"While this plant wo
uld be ready to operate soon after the end of the industrial action, there will still be the possibility of disruption to production which is currently 725,000 barrels of crude oil and 80 million cubic metres of gas per day," he said.
"This could place a substantial penalty on upstream production and could affect almost a third of oil producers in Scotland, none of whom are party to the current dispute between Ineos and Unite."
A BP official said tonight that the Kinneil plant, close to the Grangemouth complex, relied on steam and electricity from Ineos for power.
It may be possible to keep the Kinneil plant operating by other means, he said.
But if that was not possible, production would have to shut down, affecting some North Sea oilfields.
"They (the fields) would have to stop producing."
But he added some fields might have the ability to store their output.
In his statement to the Scottish Parliament, Mr Swinney said the Scottish Government still hoped the dispute could be resolved by "constructive and urgent dialogue".
He said he and the First Minister had urged management and unions to take part in talks.
It has also arranged for an independent pensions expert, Stewart Ritchie, president of the Faculty of Actuaries, to "clarify" the issues for the benefit of both sides.
The process of shutting down the plan ahead of this weekend's action began last Friday, and it would take time for the plant to resume production.
As a result of the agreements made at ACAS, resumption of fuel production should take place within days.
The full article contains 336 words and appears in The Scotsman newspaper.
