The First Minister was asked on Thursday to "shed light" on why the beleaguered probe, initiated seven years ago, has now cost £12.5 million of public money.
It has been given an extra £500,000 in next year’s Scottish Budget.
Alex Salmond, who was then first minister, promised a "swift and thorough inquiry" when it was announced in 2014.
Speaking at First Minister's Questions in Holyrood, Conservative MSP Sue Webber said a "once beleaguered project is now a much beleaguered public inquiry".
She said: "Edinburgh residents deserve answers to what went wrong with the building of the trams.
"Will the First Minister shed light as to why an inquiry that was initiated by her predecessor seven years ago is still ongoing when closing submissions concluded in 2018."
Ms Sturgeon said the probe was a "statutory public inquiry convened by Lord Hardie".
She said: "I'm not sure if the member is genuinely asking me as a minister to interfere in the conduct of an independent, statutory public inquiry.
"That would be deeply inappropriate and, let me just hazard a guess here, that if I ever did so, the Tories would be the first ones on their feet complaining about the fact that I did so.
"The judge will take forward the public inquiry in whatever way the judge sees fit and will provide conclusions.
"And at that point, I'm sure Parliament will consider and scrutinise those conclusions."