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 said.
'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.'
Allardyce may have been struck down by the virus but Blackburn believe that the swine flu outbreak within the club is under control.
Rovers looked far from under the weather in their 5-2 Carling Cup victory over Peterborough last night, despite the build-up to the match being dominated by talk of their ill players.
On Monday Allardyce confirmed that three unnamed members of his squad had come down with swine flu and that it had been within the camp for a number of days.
Fighting fit: Michel Salgado scores for Blackburn against Peterborough last night
But there was little evidence of any ill effects amongst those playing in last night's match - including suspected victim David Dunn, who came off the substitutes' bench - and afterwards assistant manager Neil 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.'
The Health Protection Agency has warned players that spitting on the pitch could increase the risk of passing on infection during matches and McDonald said that the club was doing everything in its power to ensure the virus did not spread.
Four little pigs: Cheeky Peterborough United fans wear face masks in the stands to highlight an outbreak of swine flu among the home side's squad
'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,' he said.
'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.'
A spokesman for Blackburn confirmed that Allardyce was not at the club's training ground this morning but would be back at work tomorrow. The spokesman said: 'He (Allardyce) said he would just be off today - but everybody is off today and will be back in tomorrow.
'Every time after a game, especially after a night match, they have the day off. Only the players that were not involved in the game will be in today.'
Blackburn were pegged back twice by Peterborough having gone 1-0 and 2-1 ahead, but with the Coca-Cola Championship side reduced to 10-men after goalkeeper Joe Lewis was sent off, Rovers soon powered ahead to seal a comprehensive 5-2 victory and a place in the quarter-finals.
No worries: Benni McCarthy scores Blackburn's fourth at Ewood Park last night
Summer signing Nicola Kalinic scored the fifth from the penalty spot - his first goal in English football - and McDonald said the Croatian striker was adapting well after his move from Hadjuk Split.
'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.'
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