Triesman resigned on Sunday as head of both the bid and the FA after he was secretly recorded telling a friend Spain would support Russia's bid for the 2018 World Cup in return for help bribing referees in South Africa.
FIFA's ethics committee are to investigate the corruption claims but Manchester United chief executive Gill, an original member of the England 2018 World Cup executive board now on its advisory group, said he thought the bid would bounce back following Triesman's swift exit.
"I think the action that was taken was decisive, it was immediate and it was clear and we've got to move on," Gill said in New York last night following a press conference to promote Manchester United's four-game North American Tour this summer.
"I'm sure that it can get back on track. There are some very good people leading it. Geoff Thompson, the chairman of the bid company, is very well known in FIFA and UEFA, very well respected in those two bodies and I think he's got a good executive team in (bid chief executive) Andy Anson and the supporting people like (international president) David Dein.
"So that's all I want to say on it, it's back on track and the action was decisive."
Gill also reacted with amusement to Wigan chairman Dave Whelan's suggestion the Manchester United chief executive would make an ideal candidate to lead the FA following Lord Triesman's departure.
"That's news to me, I've been travelling but it's unlikely," Gill said. "I've got a great job here with Manchester United, it's a great team, lots to go for and I'm enjoying it immensely."
Meanwhile, Sebastian Coe has reiterated his belief that the Triesman affair has not inflicted terminal damage on England's bid.
Coe, chairman of the London 2012 Olympics, is on the 2018 bid board and insists England's bid remains strong.
"I don't think anybody anywhere in the world, including FIFA, doubts that we have anything other than the great ability to deliver a fantastic World Cup," Coe told BBC Breakfast.
"This does not become a bad bid overnight."
FIFA will announce the hosts of the 2018 and 2022 tournaments, with the former anticipated to go to Europe, on December 2.
Coe, who masterminded London 2012's successful bid to host the Olympic Games, said the bidding process is fraught with ups and downs.
"I understand campaigns," he added.
"We were bidding to stage an Olympic Games for the best part of three years.
"Campaigns are marathons, they're not sprints.
"There's rarely anything that is so serious or so great that you are permanently derailed or you jump across the line in one foul swoop.
"You have to be consistent with your messages. What is the consistent message we will be pumping between now and the vote in Zurich is that we have stadiums in place that are extraordinary, we have passionate fans, we have a marketplace for football."