Surrey batsman Maynard died last summer at the age of 23 when he was electrocuted on a railway line in the early hours of the morning while apparently attempting to avoid police who suspected he was driving under the influence of alcohol.
Tests subsequently showed Maynard was a regular user of recreational drugs, something which Dernbach says nobody was aware of.
"I'd welcome a lot more drug testing," Dernbach told the Daily Mail. "If we can avoid this circumstance ever happening again, then it will benefit everyone.
"Whether it be hair testing or more frequent testing, I think all professional sportsmen would welcome that into our game.
"It's important that lessons are learned from what happened to Tommy. It's important that clubs pay attention to the more personal side of players, not just as professionals but as human beings - understanding what everyone is going through."
Dernbach, 27, was out the same night that Maynard died.
"I ask myself if I should have spotted something," said Dernbach. "Should I have seen the signs that Tommy was taking drugs? But in a professional environment you just don't think that sort of thing happens.
"Just because someone is a different character, do you have to say, 'You're a bit extrovert, do you take drugs? Where do you draw the line?
"People say, 'Why didn't you know? I understand that but hundreds of people came in contact with Tommy over his life and nobody knew. I don't know enough about drugs to understand what the signs are. If nobody else had an idea, why should I have done?"
Dernbach's England teammate Luke Wright has also called for more testing in the sport.