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The 21-year-old, who upset fifth seed Stan Wawrinka on Monday, lost 6-4 6-2 3-6 2-6 6-3 to Belgian Ruben Bemelmans.
The Russian led 2-0 in the decider but became angry at Alves' decisions as he lost five straight games and was docked a point by the umpire.
"I was just frustrated - it has no meaning, I apologise," said Medvedev.
As he was packing up, Medvedev took out his wallet and threw coins at the bottom of the umpire's chair as Alves departed. The world number 49 then left the court without retrieving the money.
He had asked for Alves to be removed in the fifth set but his request was turned down by the match supervisor. Medvedev claims he does not remember what he said during the match.
When asked whether he understood his actions could be interpreted as implying Alves was biased, Medvedev said: "I haven't thought about it and that's not why I did it.
"I was frustrated to lose the match - maybe there were some bad calls, it can happen in sports.
"I was just disappointed and [did] a stupid thing."
Medvedev added it was "not for me to decide" whether he will receive any sanction for his actions.
Bemelmans will face South Africa's Kevin Anderson in the third round.
Daniil Medvedev has denied he was accusing umpire Mariana Alves of bias by throwing coins at her chair after his second-round defeat at Wimbledon.