Two goals of real quality from Tom Adeyemi and Marcello Trotta in each half saw the Bees record their first success in eight to stay in the play-off pack.
Kernaghan hopes the win will provide the springboard for another lengthy unbeaten run like the one they put together before Christmas.
He said: "It was important to get the three points after a slight blip and now we will be looking to string a decent run together once again.
"We huffed and puffed a little and the pitch meant we couldn't play the kind of free flowing football we wanted but in the end we got a better result than we did when we've played better."
Kernaghan, who with manager Uwe Rosler travel to Chelsea on Sunday in the FA Cup, added: "We now have a game that we won't need to motivate the players at all. In many respects it's the easiest game of the week.
"But the league is where it matters and we have had our blip in mid-season. Now we enter the second stage of the campaign and we have all the top teams again and we have a good record against them."
- Sports & Recreation
- Marcello Trotta
- Tom Adeyemi