Their latest victory, a 25-14 win over Leinster on Friday night, kick-started a run of three consecutive games in front of their home fans at Parc y Scarlets.
Next up is the visit of table-toppers Munster on Friday and Edwards knows they have to keep momentum going.
Like head coach Wayne Pivac, the 35-year-old agrees that Scarlets still have improvements to make although he knows results were the main target.
"We've got Munster this week. They have a good set piece; a similar team to Leinster and it's a top of the league clash," he said.
"We have two home games - it's huge, and we've got the international boys coming back. Hopefully when you're top of the league people are a bit more wary.
"We're quite proud of our record at home, we want people to fear coming here. We do have a few things to work on in the week.
"Having said that we'll take the win. We won last week - we weren't very good but we won. If we get it right I think we'll give someone a good thumping."
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