Kevin Schade and Yoane Wissa struck the goals for the Bees.
“I’m very pleased with the win against a good opponent that have done so well here,” said Frank.
“I thought we were very robust, in many ways it was a good away performance; something we’ve done fantastically over recent away games.
“Defensively, very good. Overall, I think we gave basically nothing away in terms of big chances.
“You always want more and being a bit better on the ball, but that happens sometimes. You need to work hard, you need to be solid, you need to find a way to win, and we did.”
Just a massive win - Collins
Meanwhile, Bees defender Nathan Collins was pleased to shut out Forest's attack.
He also said: "It was a tough game, a very tough game. I think we had every season out there, too - we had a nice sunny day, then the wind, the rain... we were just missing the snow!
"It was a great win, a massive win. Forest took a lot out of us, they tested us really hard. To come to a ground like this, where Forest have been unbelievable this season, they've hurt so many big teams, so to come out with a win and a clean sheet is fantastic."
On his assist for Kevin Schade's strike, he added: "With players that can come to feet but also go behind, as a defender, you don't want to play against that, I know how hard that is.
"We work on it a lot, we look at runs in behind, I saw a little gap, I tried to put the ball there, and Kev did the rest!"