A foul by Kyle McFadzean on Kadeem Harris gave former Everton midfielder Forshaw the opportunity to break the deadlock and Kernaghan felt his players went on to take maximum points with an excellent defensive display.
He said: "We looked solid defensively and limited Crawley to only one or two chances in the second half.
"We might have exploited our counter-attacking better at times as Harris was a threat for us, but overall we deserved the win."
Brentford went into the clash at the Checkatrade.Com Stadium with an unchanged team and Kernaghan believes they are reaping the reward for a settled side.
He added: "The results have backed that up. We are fielding a settled team and things are moving along."
Brentford were forced to bring on substitute Toumani Diagouraga at half-time when George Saville had to withdraw through illness.
Kernaghan added: "George wasn't in great shape. He was looking leggy at times and the decision was made for us."