On Thursday Michael Matheson admitted an Â£11,000 data roaming charge was caused by his sons watching football while on a family holiday in Morocco.
He informed Humza Yousaf of the truth on Tuesday after initially insisting the device had been used for parliamentary work.
Opposition leaders have called on Mr Matheson to resign.
The bill was initially going to be picked up by the Scottish Parliament, but the health secretary has since paid the money back and said he has referred himself for further investigation.
OnBBC Radio 4's Broadcasting Houseprogramme on Sunday, Mr Yousaf was asked if Mr Matheson misled him.
"No, I don't believe Michael did," he said.
The first minister added that his health secretary had only used the iPad himself for parliamentary purposes and only discovered his sons' use of the data on Thursday, 9 November.
"There's a legitimate question that people have asked, and Michael addressed last week, around whether he at that point should have been upfront publicly around the fact that was the reason that he was choosing to repay the entire bill," Mr Yousaf said.
"He was trying to protect his children. For me, Michael - who I have know for well over 15 years - is a man of integrity, honesty."
He said Mr Matheson could have handled the situation better, but said he had apologised for that.
Scottish Conservative leader Douglas Ross said Mr Matheson was "hiding away" from scrutiny.
The Moray MP said only his party had the numbers to bring forward a motion of no confidence in the health secretary.
Appearing onBBC Scotland's Sunday Show, he commented on the fact that neither Mr Yousaf, Mr Matheson or the deputy first minister had agreed to appear on the programme.
"This is affecting all levels of government in Scotland because none of them are willing to come on to speak about really important issues," Mr Ross said.
"Because they can't and won't defend this health secretary, who should have resigned by now, and Humza Yousaf should have sacked him.
"The man in charge of the NHS in Scotland isn't putting himself forward for scrutiny," he added.
The former chairman of the committee on standards in public life, Sir Alistair Graham, said the health secretary may be subject to some disciplinary action.
"It was the cover-up that was the problem," he said. "He didn't tell the truth straight away.
"He didn't meet the standards that you expect from members of parliament, whether that's in Westminster or in the devolved authority."
Mr Matheson - who was visibly emotional during a statement to parliament earlier this week - told MSPs he was not aware that other family members had used the device until Thursday 9 November, after the first media reports about the charges emerged.
He said the iPad itself had not been used by his children but had been used as a hotspot to allow internet access for other devices.
The health secretary said he did not mention this in his statement on 10 November because he wanted to protect his children.
Scottish Labour leader Anas Sarwar also appeared on the Sunday Show, repeating his call for the health secretary to resign.
"I have got every sympathy for a parent with teenage children, I've got two teenage children myself," Mr Sarwar said.
"This is not about the data, it's not about his family - this is about him misleading the public. That is why I think he should resign."
Mr Sarwar said the health secretary and the first minister continued to tell "mistruths" days after each said they learned the truth about the bill.
"That's not acceptable in public life," he said.
A spokesperson for the SNP said Mr Matheson had reimbursed the parliament in full for the costs incurred and had referred himself to the Scottish Parliament Corporate Body.
"Opposition parties and MSPs are free to raise all such questions in parliament, and scrutinise ministers according to Holyrood's processes of accountability," they said.
It's been a week of technicalities when it comes to Michael Matheson's iPad.
But as facts about gigabytes and hotspots are nailed down - the essentials come to the fore; the raw politics.
Perhaps nothing is more fundamental than trust - the trust we place in our elected politicians to make decisions for us and look after our health and safety as citizens.
As well as trust, we need to have confidence in those we place in positions of power.
Trust and confidence are things that seem to have evaporated from a man once regarded as a safe pair of hands.
On trust, Mr Matheson was not accurate when he spoke to journalists on Monday saying family members had not used the device.
On confidence, do people think he's focused on the health service and its smooth running as the future of his career hangs in the balance?
Mr Matheson will find it hard to escape this topic if he's, for example, on a visit to a hospital.
The first minister thinks he could have handled it better but still trusts him.
The opposition don't - and want him out of office.
I understand the Conservatives want more answers from the health secretary before pushing for a motion of no confidence - so that looks more likely later in the week.
The first minister has said he does not believe he was misled by his health secretary over his Â£11,000 iPad bill.