The Government has ordered 8,000 additional ventilators to boost the stock of 8,000 already available to the NHS.
A No 10 spokespeson said officials did not get emails inviting the UK to join the EU scheme, and it could opt in to future schemes.
It sparked calls from opposition MPs - including Liberal Democrat Layla Moran - that the Government is putting Brexit ideology over demand for essential equipment.
Speaking on The Andrew Marr Show on the BBC, Mr Gove said: "There was some confusion over our involvement in that scheme.
"But I've talked to senior figures in the NHS and they've reassured me that there is nothing that we can't do as an independent nation that being part of that scheme would have allowed us to do."
Quizzed on whether an email was received by the Government, Mr Gove said: "There was some communication confusion, I don't know all the details of that".
He added: "I do know having talked to senior figures in the NHS that there's nothing that participating in that scheme would have allowed us to do that we have not been able to do ourselves."
Mr Gove also issued an apology to a company which said it did not receive a reply from the Government, having offered to procure ventilators for the NHS.
An NHS supplier in Nantwich said that in the international market it had found 25,000 ventilators which it could have procured for the Government.
The supplier said that having asked the Government if it wanted the ventilators, it did not receive a reply.
Mr Gove told Andrew Marr: "I'm very sorry if that company says that it didn't get a reply, I'll investigate as soon as I've stopped talking to you.
"It is the case that for companies that have got in touch with the Government, those offers of help have been forwarded to the relevant people in the NHS and in other aspects of Government, in order to make sure we secure those supplies."
Mr Gove added that the company could "get in touch directly" and said "we'll investigate".
The Cabinet minister said: "There have been some cases where people had hoped they might be able to help, but in fact the material that they produce has not met the NHS specifications".
He continued: "We have been following up every single lead presented to us."
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