NHS Lanarkshire was told to make a broad range of improvements at three of its hospitals following a rapid review into patient safety.
Health Secretary Alex Neil ordered the review in August last year after data showed each of the hospitals had had a mortality ratio significantly higher than the Scottish average at some point in the previous 18 months.
Chief executive Ian Ross and Dr Iain Wallace, medical director of NHS Lanarkshire, appeared at Holyrood's Health Committee to update MSPs on the implementation of the review's recommendations.
Committee members questioned why greater progress had not been made prior to the review, given that concerns around mortality rates had become apparent as early as 2011.
Labour MSP Dr Richard Simpson said: "Leaving aside the current report, there have been three action plans between then (2011) and now.
"Are we going to have confidence in the current plan and can you explain why the previous plans singularly failed to make a difference?"
Referring to the rapid review, committee convenor Duncan McNeil said: "You were able to come up with over 100 points for action and 21 recommendations that you are all willingly accepting... why couldn't we have applied that sort of ambition and drive previously, and who is responsible for that, previous to the review?
He added: "We have got a lot of senior people there still. How can we be assured that those people in senior positions have changed their mindset? Their record up until now has not been great."
Mr Ross said "significant progress" had been made since the rapid review was concluded at the end of last year, including the creation of a patient safety team and investment in more nurses.
"It is not as though it just started at the rapid review," he said. "Work has been going on constantly to try and improve.
"What the rapid review indicated was that we were not making progress quick enough.
"All of us regret within NHS Lanarkshire that we didn't make improvements quick enough and that we lost the confidence perhaps of some of our patients and some of our public."
Mr McNeil said: "The criticism you are prepared to accept is that (earlier action) didn't fail, it was just slow in achieving its targets."
Conservative MSP Jackson Carlaw quizzed Mr Ross on the issue further, asking if he now had "a grip" on action on patient safety.
"I think I would want to assure yourself Mr Carlaw and the rest of the committee that we do have a grip," Mr Ross replied.
The committee later heard from the Health Secretary, who said: "It is clear that staff at NHS Lanarkshire at all levels have put in a significant amount of commitment and energy into making changes, and it is essential that this momentum and leadership focus is maintained moving forward.
"I am pleased that the focus on patient safety and quality of care has increased significantly in recent months, and I am reassured that this focus will continue."
Mr Neil said there were still some areas for improvement, adding: "I have made it clear to NHS Lanarkshire that I expect to see further progress in these areas, and the Governance and Improvement Support Team will continue to offer support to help the health board make this progress.