Rovers claimed a 5-2 victory over the Championship side to book their place in the quarter-finals of the Carling Cup.
The Ewood Park outfit are recovering from a bout of swine flu which has affected the club, and Allardyce spent the whole of Tuesday's match in the stands rather than on the touchline because he was feeling unwell.
"He is feeling a little unwell, so he sat upstairs as he wanted to see the picture from above," McDonald told Sky Sports.
"He trusts in his staff which is excellent, and he was at the game but he didn't want to take any chances.
"He shot out just to make sure nobody gets what he might have."
McDonald said there were no new cases to report of players having fallen sick.
"It's under control. We had a squad up on Monday and everyone came through from that squad which was great," McDonald said.
"We will monitor it on a 24-hour basis. Everyone seems okay."
A spokesman for Blackburn confirmed that Allardyce was not at the club's training ground on Wednesday but would be back at work on Thursday.