Sturgeon said last week's contact for difference (CfD) auctions show the cost of energy is coming down, but she warned the budget for offshore projects was insufficient to grow the sector.
Mainstream Renewable Power's 448MW Neart Na Gaoithe off the east coast of Scotland was just one of two projects to be awarded CfD's in the auction.
Neart Na Gaiothe agreed a price of £114.39/MWh (€156.89/MWh) for the power it produced, less than the 714MW East Anglia One project, which also gained a CfD, and much lower than the maximum agreed price of £155/MWh (€212.69/MWh) previously set by the government.
Sturgeon said the UK government must show "greater ambition" in the Scottish offshore sector.
"We are already seeing cost reductions in offshore wind, but the scale of growth planned for the sector will be a key driver to delivering further cost reductions for the long-term benefit of consumers.
"It is essential that the UK government provide confidence to the offshore wind industry, that sufficient money will be available in future allocation rounds to allow the sector to move forward with assurance and enable costs to be further reduced," she added.
It was only six months ago that Nicola Sturgeon, then deputy first minister, was fighting for autonomous control of Scottish offshore wind projects as the country was gripped by a referendum on Scottish independence.
Her predecessor Alex Salmond said he wanted Scotland to be the Saudi Arabia of renewable energy but many experts said it would be difficult without support from the rest of the UK.
Scotland has an offshore pipeline of approximately 5GW, but with the recent CfDs only supporting one project, doubt now hangs over the 1.1GW Moray Firth and 784MW Inch Cape projects.
The 664MW Beatrice project, developed by Repsol and SSE, was handed a final investment decision enabling contract for difference subsidy in summer 2014.
During the independence campaign, there were repeated warnings the UK would stop support for Scottish projects if the country split from the rest of the UK. Salmond refuted the claims, saying the rest of the UK was dependent on Scotland's renewable power to reach its European targets.