"I think we just really needed to win that a lot more. We've played a lot of good rugby without the results. We were making the point to the boys during the week that we missed two kicks which could have changed everything else.
"We missed gainst the Dragons and then there was one against Cardiff. If they'd gone over, wee'd have two other wins and tonight would have been first versus third.
"We placed it in that light and I thought we did play some good rugby."
The Australian paid tribute to Ulster's improved discipline and defensive solidity, as well as giving special mention to two-try hero Timoci Nagusa.
"We were much more disciplined apart from the sin-binning (for Ryan Caldwell) which I thought was silly from us.
"Our biggest plus (tonight) was our defence which I thought was superb. To keep Munster tryless, not many other teams can do that."
He added: "Three things have been killing us - penalties, our missed tackles and our individual turnover rate.
"They were all into double figures. I haven't seen the figures (tonight) but I would suggest that all of those are in single figures. When you have that, you take a win. Probably Munster missed a few more tackles than us.
"I thought Timoci (Nagusa) played well, but the other great thing tonight was that we had nine players in our 22 who were 22 years and under.
"It's a pretty staggering feat for the future for the province and to get a bit of confidence out of a game like that going into a break (for the autumn internationals) is fantastic for us."
It has been a very encouraging week for Ulster Rugby, with international winger Andrew Trimble putting pen to paper on a new two-year contract and now taking the scalp of the Heineken Cup champions.
Williams remains confident that this current crop of youngsters will bring success back to the province and make Ravenhill a fortress once again.
"I'm old enough to know the score, it doesn't matter who the coach in Ulster is they still have the same job.
"Because of where it is, we have got too many players of the one generation coming through and that's just the way it is.
"When you have a young team - as you would have seen in the last eight weeks - if you watched us playing against Stade (Francais) and playing against Harlequins, we actually did play some good rugby in periods.
"We were very inconsistent (though) and tonight was probably our most consistent 80 minutes, apart from Cardiff.
"When you do that at home and you do finish off, and give the ball into the hands of someone like Timoci, who is electric and is coming into form, you get the wins," he explained.
For a full match report on Ulster v Munster, click here.