But Wales know that victory in Dublin would keep alive chances of retaining their RBS 6 Nations crown.
Whether Johnson stays after the tournament remains uncertain, yet British & Irish Lions flanker Williams believes Wales cannot afford to lose him.
"It is hugely important that Scott stays (beyond the Six Nations)," he said. "Personally, I can't put a value on him - he would be a massive loss to us.
"He has turned us around in terms of our skills and how we look at game analysis. He is just at a different level to anything I have come across before.
"He is definitely the best coach I have come across, without a shadow of a doubt.
"Hopefully, whatever happens in the next three games he will stay anyway, but if we could have a bit of a success, it would take a lot off everyone, both on and off the field."
A win would go some way towards restoring a degree of normality in the Wales set-up, but Thomas' absence - he was taken ill last Sunday night suffering from a severe migraine - means it would be achieved the hard way.
"A lot of guys, as soon as they become captain, try to change their character and personality, but 'Alfie' has just been exactly the same, which rubs off so well on the boys," said Williams.
"He is definitely a players' player. He doesn't side with anyone, and his whole ethos is the players must come first.
"He leads by example, and he is also one of the greatest players about. The biggest thing now is that he gets back playing again, but not to rush things.
"Scott Johnson is exactly the same. Although he has gone to number one (coach), you can hardly tell the difference because his approach is exactly the same.
"As Scott told us, you have got to front-up to the situation, you can't brush it under the carpet. He called all the guys in and explained where he was coming from and what he expected from us this week.
"Like he said, the most important thing is we win a Test match on Sunday and forget about what is going on off the field.
"In Wales you are always under the microscope every Test match, and this is even more so. The eyes of the rugby world are probably upon us, so it is an interesting one.
"But it has galvanised us as a squad, so it is up to us really to try to deliver the goods on Sunday."