"This will not affect the business in any way," he told Pravda TV.
"Manchester United is not just about two people, it is about the strength of the team, on and off the pitch.
"We have many people here with many years' experience with the club. Manchester United has been around for many years and will continue to be successful.
"We wish Nick and Andy well and we would have preferred this had not happened but we will move on. We still have a great future ahead of us."
It is believed both men have already secured alternative employment, with Gill accepting their departures will leave a big hole.
"Nick and Andy have made a great contribution to the success of Manchester United over the last few years," He said.
"I am disappointed but I recognise they wanted to move on for new challenges.
"It's strange they are both leaving at the same time but you cannot legislate for that."
Meanwhile the Glazers thanked the duo for their work at the club.
"The Glazers would like to thank Nick and Andy for their contribution and support during the last 18 months," a spokesman for the Glazer family stated.
"They leave the club in excellent shape and we wish them well."