New business levels also "stagnated" during October and volumes of incomplete work dropped.
The Bank of Scotland PMI survey showed companies added to their payrolls for the third successive month.
That was despite firms facing the sharpest increase in input costs since September 2011.
A further rise in output charges was reported, although the rate of inflation was weaker than that for input costs.
Seasonally-adjusted figures showed Scotland's private sector grew for a second successive month.
The increase in output was spread across manufacturers and service providers, with both reporting "marginal growth" in business activity levels.
The PMI panel members said companies' cost prices increased at the sharpest rate for more than five years as a consequence of a drop in the strength of the pound.
Nick Laird, the regional managing director of Bank of Scotland Commercial Banking, said: "Output for Scottish private sector companies continued to show growth in October, albeit at a reduced rate weighed down by a combination of higher input prices and stagnating new business.
"The increasing cost burden is a cause for concern, with the rise in input costs growing at the quickest rate in just over five years attributed to the depreciation of Sterling.
"Encouragingly, workforce numbers rose for a third consecutive month. Yet with a further solid decline in backlogs of work recorded, we could see jobs growth come under pressure towards the end of the year."
The expansion of Scotland's private sector has slowed down while output growth has weakened, according to a report.