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 touchlines because he was feeling unwell.
"He is feeling a little unwell, so he sat upstairs as he wanted to see the picture from above," said McDonald.
"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."
On the swine flu, McDonald said: "It's under control. We had a squad up on Monday and everyone came through from that squad which was great.
"We will monitor it on a 24-hour basis. Everyone seems okay.
"I'm not a medic so I don't know how it is passed on, but you can spit, cough, sneeze - anything that comes out of your body is how it is passed on I suppose.
"I think there is always a problem in it spreading, but we are doing our best to try and contain everything by doing the right things and monitoring everyone, and we will continue to do that.
"Hopefully it won't spread any more, fingers crossed."
KalinicMcDonald was happy to see new Croatian signing Nicola Kalinic grab his first goal in Blackburn's colours.
"He has created a couple of good chances and to get that first goal will take the pressure off him of course - but that's against Peterborough," said McDonald.
"It takes time for a foreigner to come into our English game and adjust to the pace, to the style of play and the physical and mental demands.
"He has been patient and we have seen glimpses of what he can do certainly. He'll only get stronger I'm sure."