The High Street baker also said the price of ingredients and supplies was rising.
But Greggs said it was confident about future trading.
It said it would accelerate its store openings to 150 a year as part of an “ambitious” target to double turnover over next five years to about £2.4bn.
In a trading update, Greggs said like-for-like sales increased by 3.5% in the third quarter of the year, against the same period a year earlier.
It meant its full-year trading performance is likely to beat the company’s previous guidance to investors.
But the company, which has more than 2,100 shops but now plans to hit 3,000 over the next few years, said it had “not been immune” to well-publicised supply chain pressures affecting the UK’s food and drinks firms.
Greggs also warned it expected costs to climb over the next few months.
“Food input inflation pressures are also increasing – whilst we have short-term protection as a result of our forward buying positions we expect costs to increase towards the end of 2021 and into 2022,” the group said.
“Supply chain issues and labour shortages remain a key risk for Greggs with no end in sight. Temporary interruptions for some ingredients could result in the Group reducing its range and would hamper current momentum.
Ross Hindle, analyst at Third Bridge, said: “From a pricing point of view, Greggs chose to pass on the chancellor’s VAT discount to their customers. They now face the tricky challenge of putting their prices back up when VAT increases to 12.5% at the end of September, and 20% in 2022.
“This may mean short-term margin pressure for the group especially in the face of rising inflation.”