Williams said: "It is very much a case of keeping with the same 22, we need to finish the job that we started in France and it is up to the same group of players to finish it this week."
Ulster, who were much improved in their first half performance against Bourgoin, provided the management and supporters with lots of positives.
"We led for most of the game and we now know what allowed them back in - it was us and not them that made the errors. We all have a clear idea in our minds what we need to do on Friday night," Williams added.
Ulster are currently at the bottom of the Magners League table with Connacht just one point above them. Connacht have not beaten Ulster for almost two years and a win for Ulster would see the western province drop to the bottom of the league.
ULSTER (v Connacht): Mark Bartholomeusz; Tommy Bowe, Andrew Trimble, Paul Steinmetz, Simon Danielli; Paul Wallace, Isaac Boss; Justin Fitzpatrick, Rory Best (capt), Bryan Young, Matt McCullough, Carlo Del Fava, Neil Best, Kieron Dawson, Roger Wilson.
Replacements: Nigel Brady, Declan Fitzpatrick, Ryan Caldwell, Declan Pollock, Kieran Campbell, Niall O'Connor, Rob Dewey.