The in-form Londoners produced a clinical display at the City Ground with Liam Trotter, Darius Henderson, Chris Wood and substitute Andy Keogh all finding the target.
But Gallen says it is imperative that the Lions do not get over-excited about their fine performance.
"The important thing is for us not to get carried away with it," said Gallen.
"It's a massive achievement to come to a place like this, score four goals and beat Forest. When you see the team that Forest put on the pitch they are very impressive and then you get more worried at the quality they have to come off the bench.
"But, while our fans and everyone connected with the club can feel pretty pleased with the way things have gone today, by tomorrow it will be all over.
"We have a tough game against Watford on Tuesday night and we have not beaten them in our last four meetings, so we will go there and try and do something about that.
"The big issue for us is not to get carried away because, if you do that in this league, you come unstuck."