The club has also rallied around defender Joshua Inserra, who is sidelined after suffering internal injuries in last week's Melbourne derby.
Victory (0-1-1) are still seeking their first league win under new coach Giovanni Savarese and host Central Coast Mariners at AAMI Park on Sunday, before playing Persib at AAMI Park next Wednesday.
"Of course, we are having not a good good path right now," former Auckland star May said.
"These two games are important for us to get two wins, settle in in both tournaments.
"So I have to be important. I showed this in in Auckland, and I have to show it here."
May and skipper Jason Davidson didn't travel to Indonesia for the midweek ACL2 trip, where Victory lost 2-0 to Persib.
The former Auckland playmaker is fresh and confident he can build chemistry with striker Charles Nduka, while May urged Victory to wipe out recent second-half drop-offs.
"Maybe we have to maintain our structure in the second half. Be more ruthless in front of goal, take better decisions in the final third," May said.
"We have to take better decisions, and I have an important role on the team, so I have to do it better."
Savarese was confident Victory were showing the right signs but needed to tidy up their work in both boxes.
"I'm very content and happy and excited about the way we play and how we are confident with the ball and the type of football that we are able to produce," he said.
"But the game is beyond only football and good football. It's about winning as well."
Inserra was forced off late in last Saturday's 1-1 draw with Melbourne City, initially with a back injury, and later hospitalised.
Savarese confirmed the 21-year-old had also suffered unspecified internal injuries.
"It's a delicate situation that he has," Savarese said.
"We need to understand fully everything before we give all the information, and it's something that is going to keep him away for a few weeks.
"But shortly we will be able to explain exactly what it is.
"But he had to be hospitalised for the situation and it's very unfortunate.
"It has to do with organs. It has to do with something a little bit internal."
May said players had visited Inserra while he was in hospital while Savarese confirmed the defender was now back spending time around his teammates.
For Sunday's match against the winless Mariners, Victory will welcome back midfielder Louis D'Arrigo from a hamstring injury.
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