The victory lifted Ospreys up to third in the RaboDirect PRO12 table ahead of the next meeting between the two sides at the Liberty Stadium on Friday night.
And despite holding home advantage, Biggar knows it is unlikely to be any easier against their Welsh rivals.
"It's never easy, they always play with an intensity that we know they will bring to the game, but we struggled to adapt early on," he said.
"We didn't start well but it's credit to the boys for managing to hang on in there and fair play, it was a great effort to get the try.
"It was a three point game going into the last ten minutes and that's what you expect playing against the Scarlets here.
"It's always going to be tight but we kept going and when we needed to be accurate we were.
"We managed to kick to the corner and our lineout was effective
"When it mattered the forwards were outstanding and that try at the end was perfect.
"We defended well after that at the end and when we needed to be accurate we were.
"It wasn't free flowing rugby at times out there but that's what you expect from a derby game."
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