Costa has reported a fall in profits and a slowdown in sales at its existing coffee shops in the last six months.
Pre-tax profits at Costa slid 10% to £59m, with the UK's biggest coffee chain saying it was partly due to more expensive coffee imports.
However, the firm's owner, Whitbread, saw group profits rise thanks to growth from its Premier Inn hotel business.
Whitbread boss Alison Brittain said consumer confidence had "softened" slightly on the High Street.
She also told the BBC that Costa had no plans to put up its coffee prices, despite seeing rising costs.
The fall in sterling means the coffee that Costa imports - which is priced in dollars - has become more expensive, Ms Brittain said.
"There's a lot of cost pressure in the business, whether that be wages, rates, rents, inflation, which we've offset with efficiency gains," she added.
Coffee's 'third wave'
The company also pointed to investment in stores and the closure of its French business for the decline in statutory profit.
Costa's revenues in the UK increased by 8% in the six months to 31 August, but that was largely driven by the addition of 108 new stores.
Its like-for-like sales - which measures growth among existing outlets - increased by only 0.6%, down from 2.3% growth in the same period last year.
The chain hopes that what it calls the "third wave of coffee" will help to boost sales.
It described this as a period in which UK "consumers' preferences for coffee become more sophisticated and are willing to spend more per cup".
The Premier Inn hotel business fared better, with profit rising by 27% to £295m as it added more than 2,000 new rooms.
Ms Brittain said an influx of tourists coming to the UK's big cities - attracted by the weaker pound - had "left the hotel market quite buoyant".
Premier Inn is looking at international expansion, particularly in Germany where it plans to open eight new hotels.
Whitbread's group profits in the period increased by 20% to £316m on the back of 7% sales growth to £1.7bn.
The company's shares fell about 5% and are flat for the year.