The hosts paid the price for giving away too many penalties within Halfpenny's range and while Greig Laidlaw's 18 points from the tee kept his side within touching distance for the most part, Wales pulled clear in the closing stages.
And Johnson acknowledged that his side had no-one to blame for defeat but themselves, hinting that his side's starting XV against France next week could feature a number of changes.
"We're very frustrated and I've said to the team we've got to acknowledge our ills in this and we have to look at ourselves and at what we are doing wrong," said Johnson.
"We only got our first lineout in the second half and that's telling. We played once again with great heart and showed great resolve but we can't keep doing it.
"We've got to look at ourselves, I won't be blaming anyone else.
"We've spoken about the game against France and the fact is that we've got to acknowledge what we do and have a look at things and if that means making changes then we'll do so.
"We're going to Paris to compete though, don't you worry about that."