Rovers were pushed all the way by their Championship opponents in the third round of the Carling Cup, and were fortunate to leave the City Ground as victors.
Despite Forest's dominance they were unable to force a breakthrough, even missing a second half penalty through Dexter Blackstock, and the game was eventually settled by Benni McCarthy's 37th minute free-kick.
Allardyce was delighted to see his South African frontman on the scoresheet and was pleased to have avoided the unwanted distraction of extra-time.
"Benni meant to do that, we practice it in training all the time," he said on McCarthy's whipped effort which drifted past a host of bodies before nestling in the bottom corner.
"We always practice to hit the target as the goalkeeper can't do anything about it as there's a cluster of players there that may get a touch.
"So if someone gets a touch it can go in and if someone doesn't the goalkeeper is left stranded and it goes in the back of the net.
"It's the quality of the ball from that angle to get it on target that was the difference in quality between the teams.
"That outstanding free-kick and Jason Brown's absolutely superb penalty save from a very well-taken penalty was the quality that won us the game.
"I was disappointed with the decision of the referee to give the penalty as it could have thrown us into extra-time which we wouldn't have wanted, but we overcame it I'm glad to say."
Allardyce added: "Overall I'm delighted. It was a tough match like we expected and we came through with no injury problems and gave a lot of players some really good football to catch up with match fitness.
"With a squad of our size it's important to give players some high quality time on the pitch. We made 10 changes and it disrupted the team initially as they are a group of strangers playing together, really.
"We had two exciting lads making their way in the team in Junior Hoilett and a young lad who made his debut at the back and looked like he'd played there for a number of years in Phil Jones."
Bad luckThe result was harsh on Forest, who continue to struggle on home soil, but boss Billy Davies refused to get too downhearted at the final whistle.
"It was a fantastic delivery as it is one of these goals where there's about six or seven bodies running across that goal and it can hit anybody and go anywhere and it has sneaked it at the far corner," said the Scot.
"It's a fantastic delivery but a stupid free-kick to give away."
Davies added: "We dominated and should have been well in front, we hit the bar, missed a penalty and outplayed a Premier division side.
"I have nothing but praise for the players. For whatever reason at the moment we are just in a very bad run of luck, not just one game, it has been a consistent run of bad luck since the start of the season.
"We are dominating games and playing well in my opinion, but such is life."