The Black Cats were dealt a double injury blow on Wednesday when both striker Fletcher and captain Cattermole were ruled out for the rest of the season.
The club's leading scorer suffered ankle ligament damage on international duty with Scotland, while his team-mate and skipper underwent another operation on a knee problem.
O'Neill says they cannot afford to dwell on the injuries to their key players with the club sitting just four points clear of the Premier League drop zone.
He told the Daily Mirror: "It's not great, but we'll have to get on with it. It's a blow to Fletcher, and a blow to us.
"We've just had the news through from the specialist. His ankle will have to be put in a non-weight bearing plaster or something, for about a fortnight to know whether it might have settled down or will need an operation.
"I watched the game [against Wales last Friday, in which Fletcher was injured], saw him go down and saw the stretcher go on. You fear the worst, then hope it is better news.
"You send players away on international duty and that is the risk you run. Anything can happen... and it has.
"We have to get on with it. I was watching the Republic of Ireland game last night and thankfully none of our players got injured, otherwise it would have been worse.
"It is something we could have done without at this stage of the season."