In his absence, Blackburn ended a run of 10 successive defeats on the road in the league by recording a 2-0 victory against Allardyce's former club Bolton.
Influential midfielder David Dunn made the breakthrough and Bolton's fate was sealed with a bizarre own goal from Sam Ricketts.
Allardyce will also miss matches against Fulham and Stoke and McDonald said: "Hopefully we have put a bit of a smile on his face and taken a little bit of stress away from him.
"I would like to think it will give him a chance to recover knowing his team has done well.
"Sam is a person who looks after himself. He is always having check-ups and making sure he is in good health.
"Luckily they have found it out very quickly. I am told it is routine operation, so he should be back fighting fit very soon.
"I would imagine he would be okay next week for match against Chelsea.
"I spoke to him before the game - and he spoke to the players yesterday. They all knew what they had to do. We all have to take responsibility as we are professionals."
Former Carlisle manager McDonald enjoyed being back in the dug-out. "Was I stressed? No it was easy", he joked before adding: "We are really pleased with the performance.
"We have kept a clean sheet which is a bonus. Everyone played at the top of their game. We have got rid of our away hoodoo. We worked very hard to try and change that."
McDonald praised Dunn and said: "He is absolutely fantastic, especially in possession and it was a marvellous goal.
"He is also working hard on other parts of his game. If he keeps himself fit and free from injury, he can run from the edge of the box to support players. That is a great asset to have."
Bolton manager Gary Megson was left bewildered by his side's defending and they remain in the relegation zone.
Dunn opened the scoring with his sixth goal of the season after a flowing move, which followed Matt Taylor's deflected free-kick hitting the bar for the home side.
Blackburn then sealed the game when Ricketts headed past Jussi Jaaskelainen, not realising the goalkeeper had taken a walk.
Megson said: "Jussi was not aware Sam was going to get there. But there didn't seem to be any need for Jussi to come. It was comic cuts.
"The first goal was always going to be important. When they scored it took the wind out of our sails. For us not to get a touch in the build-up is poor in the extreme. The second goal was even worse in terms of that."