Mr Byers was cleared of deliberately lying about events leading up to the collapse of Railtrack, despite admitting he had not told the truth.
But MPs said he was wrong to try to justify his incorrect answer and called on him to "apologise unreservedly".
Mr Byers admitted at the High Court last year that he had misled MPs when he claimed he had not considered Railtrack's collapse before the company first raised the matter.
The ex-Cabinet minister was being sued in an unsuccessful action by shareholders left with worthless stock in October 2001.
He had told MPs that he did not consider pulling the plug until the chairman told him the firm would collapse unless it was given more Government cash at a meeting on July 25 2001.
But lawyers produced an email sent by Treasury advisor Shriti Vadera on June 21 which said Mr Byers wanted "alternative owners and management".
Mr Byers told the court his remarks to MPs had been misleading and he could not "remember the motivations behind it".
The Standards and Privileges Committee said that, four years on, that was understandable.
But Mr Byers was wrong to suggest in an apology to the Commons that the error was caused by a misunderstanding.
"Mr Byers was unwise to try and devise retrospectively an explanation for his inaccurate answer," the committee's report said.
"We also believe that, in his personal statement, he came close to repeating the error for which he had apologised.
"Given that Mr Byers could not recall why he gave the answer he did ... he should have said so to the House in his personal statement on October 19 2005 and apologised unreservedly.
"We recommend that he now does so."
The findings are a further embarrassment to Mr Byers but leave the way clear for him to return as a minister.
The North Tyneside MP said in a statement: "I am obviously pleased that after a full investigation and having considered all the evidence, the committee has concluded that I did not lie.
"This was an extremely serious allegation which the committee has rejected in the clearest possible terms."
Mr Byers added: "I have never regretted my decision to refuse Railtrack further taxpayers' money and then to apply for it to be put into administration.
"It was quite simply the right thing to do."
Chris Grayling, who asked Mr Byers if there had been discussions about the future restructuring of Railtrack before the firm was put into administration, took the complaint to the committee.
Mr Grayling, who is now shadow transport secretary, said the MP should now heed the committee's call to apologise.
"I think he has little option but to simply say 'I'm sorry' and I hope he doesn't seek to do any more than that," he told Sky News.
"He has been cleared of lying but he has been criticised by the committee...
"He needs to apologise to the House for what happened, draw a line under it and then we can move on.
"As I say, I hope ministers learn the lessons of what has happened. They have got to be absolutely upfront and accurate at all times."
Mr Byers will make a personal statement to MPs about the findings later today.
The standards committee report also calls for the letter sent to ministers reminding them of their obligation to "truthfulness and accuracy" to fellow MPs to be amended.