The Foxes were beaten 4-1, with Kevin Schade netting a hat-trick for the hosts.
Dawson later said, "As expected. We knew coming here Brentford's home record and the crowd get behind them. We got ourselves in front with the goal and decision making in key moments have contributed to the scoreline.
"Not so much the first one but the second one we're down to 10 men and then the third just before half time. They hit hard. We showed some good play for some parts of the game.
"The thinking was trying to get three points. We've reassessed everyone and thought that was the best way to go to get three points.
"Only last night, we exchanged a few texts and we'll catch up tomorrow. Bit of a challenging afternoon. It can be a lonely place stood on that touchline but everyone was excited when the announcement was made yesterday so hopefully that positivity continues."