Tries from Ben Howard, Semisi Taulava and Jake Abbott had put Warriors in the driving seat before Best secured the maximum points with his last-minute effort.
"It was nice to come on and get the try and it was a good turnaround after the break," said Best.
"We were getting turned over at the ruck quite a lot in the first-half so we addressed that. We also tried to tighten things up in the second-half and hold onto the ball a bit more.
"It was a tight game. They are a good team and they've shown that with their performances in the league this season."
The Ireland international was making his second appearance of the season and was pleased that the side secured maximum points.
He added: "We were always looking to score four tries so it was important to do that and we just about did it in the end so we are pretty pleased.
"The emphasis all week was on scoring four tries and we were trying new things and tried to play more expansive rugby. It worked well in the end and we could have scored even more.
"Like most competitive games, the two teams were parallel with each other for most of the match and then we just pulled away from them.
"It will be all smiles in training next week and we will look forward to another tough match against London Wasps in this competition next Sunday."