An opening day win over Munster gave Glasgow just the start they wanted but Bernie says it will count for nothing if they can't follow it up against the Scarlets.
Bernie told the Glaswegian: "Great though it was to beat Munster we must guard against complacency.
"Llanelli will be a different test and we can't go in thinking that because we've beaten last season's champions, we are going to beat them as well.
"They can be dangerous too - they got a good win as well beating the Heineken Cup winners Leinster - so we again must be at our best.
"Llanelli are very good with the ball in hand so we need to put pressure on them from the start and deny them both time and space on the ball.
"The more possession we have, the less likely they are to threaten us so we need to put in another good performance like we did against Munster to win."
Skipper Alastair Kellock echoed Bernie's comments - he told the Scotsman: "Although it was a positive against Munster we can't pat ourselves on the back too much for a home victory because we should be winning all our home games.
"Having said that, I was absolutely delighted with our scrum, lineout and contact area where I thought we were ruthless. But we can improve on all three of those aspects and now the test is to put it in again, do it consistently.
"The first thing I said to Sean when I came off the park last week was that we can still be better than that ... Some things were very good and other areas we can improve on. You struggle to find the perfect game but we're aspiring to it and if we can get better every week we'll get closer to it.
"Inconsistency was the main (debilitating] factor last season. Loads of different factors affect consistency but there were two or three teams that were consistent last season and they finished in the top three. I do believe we're definitely doing the right things now to be consistent through this season and finish in the right place."