They backed up their impressive victory against Heineken Cup champions Leinster last week by inflicting defeat on the Glasgow Warriors in what was meant to be a celebratory day for the Scottish region.
The Scarlets rained on Glasgow's parade, who were making their first appearance at the refurbished Scotstoun Stadium, with a gritty 18-13 victory.
Easterby was delighted his side were able to concentrate on delivering a match-winning performance and ignore the off-field distractions surrounding the stadium.
Easterby said: "I am very proud of the way the players secured that win, they worked very hard for that victory, it was hard-fought and showed the character and commitment in this Scarlets team.
"You can't ask more from the players than to come up to Glasgow and secure a tough win especially on a big night and occasion for the Warriors and their home supporters.
"We finished off our opportunities well, our attack looked lively and to get three tries away from home was particularly encouraging; we also defended well for large chunks of the game and the boys showed solid determination and mental strength because physiologically it was always going to be a difficult game for us.
"We kept our hold on the game and executed the game plan well; we knew they'd throw everything at us on Friday night and we held firm.
"We soaked up their pressure in the second half well and I thought the boys came out of the changing room at half time with a real edge; mentally and physically we were a match for them and it takes a certain mindset to do that away from home so there's positives that we can take from that game now in our preparations for our trip to Connacht next weekend."
The former Ireland back-row forward was quick to stress that despite their unbeaten start to their RaboDirect PRO12 campaign, the Scarlets can still improve their performances.
"We've got off to a decent start in the league but it's just that, a start - and there are also some important areas of our game for us to work on going forward," said Easterby.
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