New Zealand was one of 73 countries to vote against Blatter last month, and Martin said it was "pleasing when he fell on his sword" a few days later.
He said it was now important New Zealand Football was close to the new Fifa boss, whether that was Prince Ali Bin al-Hussein, Blatter's opponent last month, or someone else.
"There will be other candidates come out of the woodwork. We've got to keep close and keep a radar on what's going on," Martin said.
He was "very disappointed" Oceania did not gain direct entry into the 2018 and 2022 World Cups, a decision announced after a Fifa executive committee meeting late last month. "We were led to believe that Blatter had almost promised it to Oceania Football Confederation president David Chung," Martin said.
"Even on the Friday in Zurich when Blatter was re-elected, his final comments talked about doing something for OFC."
Martin said it was not just about gaining a direct spot and avoiding qualification via an intercontinental playoff, but also about ensuring New Zealand had competitive games for the full four-year cycle between tournaments.
However, he confirmed New Zealand was working to organise matches against teams from the Middle East, Europe and Asia, with the "over-arching" aim of qualifying for Russia 2018.
While Martin has been enjoying the "brilliant" under 20 tournament, he is worried about the possible distraction of Blatter attending the semifinals and final, which was scheduled before Fifa became embroiled in scandal.
"It's a distraction. It's a sideshow," Martin said. "We don't think he should. If he is the president who comes, we will do what we need to do in terms of hosting him and looking after him, but it will be a sideshow and it will take away from a fantastic festival of football."
More than 170,000 people attended matches in the group stage of the tournament across the country, which was more than expected, Martin said.
He was pleased with the way the tournament had been running so far, and said he had received "great" feedback from teams, including those who had spent time in Dunedin.
"It's been brilliant. Attendance has been good, performances are good, some superstar players are around and New Zealand qualified for the next stage, which is even better."
Martin also confirmed a review of the ASB Premiership had been completed. Franchise licences expire at the end of next season, but change is imminent beyond that.
New Zealand Football will present its recommendations to the executive committee on July 2, with its eyes on a remodelled league launching late next year.
"What's important is sustainability of the competition, competitiveness and stability," Martin said. "It needs to be sustainable and ultimately it needs to be broadcastable."
- PA