After a stuttering start to the new season, the Ospreys received a big boost with a gutsy 21-18 victory against their west Wales rivals at the Parc-Y-Scarlets - a win that Williams insists shows they can grind out a result even in the most difficult of circumstances.
"It's great to win the game before beginning our European campaign," said Williams, who has seen the Ospreys reach the quarter-final stages of the last three Heineken Cups.
"It was a tough game and it was all Scarlets in the first half. We didn't know what had hit us in the first 40 minutes - to be fair to the Scarlets they came out full of fire and made it very difficult for us.
"We addressed it at half time, went out for the second half and started playing some rugby.
"We've got another tough game away from home next week against Toulon. It's going to be a tough old group for us, and a tough old season.
"But if we can win games like that - it was quite ugly in the end - away from home, then it does give us a bit of momentum going into Europe.
"We know we can play better - we'll have to next week."
If the Ospreys are to get their Pool 3 campaign off to a flying start, they will have to break with tradition and win away in France.
The Ospreys have won just once in eight previous Heineken Cup pool matches in the Republic, with their sole success coming against Bourgoin back in the 2007/08 campaign.
Williams and co have lost out to Toulouse, Castres Olympique, Clermont Auvergne (twice), Stade Francais (twice) and Pepignan on the road in the pool stages and were also beaten by Biarritz Olympique in the final eight of last year's competition.