The First Minister made the comments after she was asked about moves by UK ministers to replace European Union funding in the wake of Brexit.
She also raised “significant and profound” concerns over the Internal Market Act.
This was brought in by Westminster to regulate trade between the four nations of the UK following Brexit.
Appearing before Holyrood's conveners' group, Ms Sturgeon branded it a "power grab", insisting it could "automatically disapply" legislation passed by Holyrood.
She said: "I think it's something every member of the parliament should be absolutely up in arms about."
SNP MSP Kenneth Gibson asked Ms Sturgeon about UK ministers involving themselves “in devolved areas”, adding: “How concerned are you about the rolling back of devolution?”
The First Minister replied: "Very, I think that's the express objective of the current UK Government, is to undermine, roll back, get in the way of this parliament doing its job."
At a separate event in Holyrood, Dr Chris McCorkindale, a legal academic at the University of Strathclyde, called on MSPs to be "bold and robust" in holding ministers north and south of the border to account on the post-Brexit internal market.
He said: "There is a long-standing culture of secrecy in the UK constitution and that's not meant in a conspiratorial way.
"Just in the way in which business is done at a governmental and official level before information is shared and scrutinised through whatever parliamentary processes apply.
"And that seems to be the case when it comes to the negotiation on common frameworks or intergovernmental relations dealing with Brexit more generally.”
He added: "Parliament has to ensure that it anxiously scrutinises the claims made at the intergovernmental level, the level of information that comes out, the distinctions that are made that might avoid parliamentary scrutiny, such as that between technical and policy-related information.
"And it has to be bold in its reporting function when it feels that it's not being served adequately by mechanisms for intergovernmental relations, it's not being served adequately by the Scottish Government reporting back, then it has to be bold and robust in its reporting mechanism to make that clear and to push, almost embarrass governments at both levels into action."