Bereaved families have accused the inquiry of "protecting PPE suppliers from scrutiny", after it emerged the inquiry would not seek evidence from commercial firms involved in the contracts.
Lobby Akinnola, whose father Femi died in April 2020, said individual suppliers need to be held to account.
"If people are not called to give evidence, then how are we ever going to know what went wrong?" he asked.
"Covid cost the lives of nearly 250,000 people in the UK, and if we don't take every step we can to learn from mistakes, we are going to leave a weakness in our response."
A spokesman for the Covid inquiry said it did not need to hear evidence directly from PPE firms as the focus "is on how the government responded to suppliers' offers".
"Our role is not to pursue criminal investigations into individuals or suppliers – that is a matter for law enforcement," he said.
The inquiry also ruled in January that any sensitive evidence about PPE Medpro, the supplier linked to Baroness Michelle Mone and her husband Doug Barrowman, would be held in private to avoid prejudicing any criminal investigation.
The inquiry's chair, Baroness Hallett, has already taken evidence on other subjects including pandemic planning and political decision-making, the impact on the NHS and the vaccine rollout.
Future phases later this year will cover the care sector, test-and-trace, the impact on children, and the economy.