Mr Thompson was one of a handful of current and former BBC employees, including former chief technology officer John Linwood, giving evidence to the Public Affairs Committee about the scheme's failure.
The scheme - an attempt to create an integrated digital production and archiving system - was scrapped by current director-general Tony Hall in his first weeks in the job.
Asked about previous evidence, where he said DMI was working well, Mr Thompson told the committee: "I don't believe I have misled you on any other matter and I don't believe I misled you knowingly on this one."
He said it "failed as a project" and added that he "wanted to say sorry" for the waste of public money.
A report by the National Audit Office (NAO), published last week, was critical of the scheme and said the BBC Executive "did not have sufficient grip" on the IT project.
DMI was meant to allow staff to handle all aspects of video and audio content from their desks, but after years of difficulties - during which £125.9 million was ploughed into it - the plug was pulled last year, leaving a net cost of £98.4m.
It emerged last week that Mr Linwood, who was paid a salary of £280,000, was sacked weeks after being suspended over the multimillion-pound failure.
Mr Linwood said Mr Hall had been too hasty in writing off "tens of millions" of pounds of investment in IT.
MPs also asked Caroline Thomson, the BBC's former chief operating officer, about her pay-off, which saw her leave the corporation with around £700,000 and a £2m pension pot.
Asked if she would return some of that money, she said: "No." She said: "I was made redundant, I didn't want to be made redundant. I wanted to stay and work."