The Scot, 26, stopped Joubert in the sixth round - a ninth win out of nine.
"I had to [get] over the clash of heads and cut in the first round," he told BBC Scotland. "It's a pretty nasty cut.
"I learned I can deal with having to get cuts and when it gets rough I can carry on with it. I kept myself nice and calm."
The 2014 Glasgow Commonwealth Games gold medallist has previously stated his ambition to fight fellow Scot and WBA super-lightweight champion Ricky Burns.
Taylor's promoter, former world champion Barry McGuigan, said: "We'd love that fight. That's a great fight, that's a magnificent fight down the line.
"He [Taylor] is impressive. He's so inventive. He's creating his own little style. Taylor has got that uniqueness about him, he's just so inimitable in everything he does.
"He's great to watch and he's definitely going to go the whole way. The difficulty for me now is how do I fill the gap between here and world championship fights because that's where he's capable of going?
"I need to have something else in the middle because once you make that step, there's no turning back. You can't go back and have easier fights where you can gain experience. That's my dilemma."
And Taylor added: "I'm quite happy where I am just now, maybe another defence of the Commonwealth, maybe even knock on the door of the European [title].
"I learned a lot about myself [against Joubert]. I was impressed with my own performance.
"I caught him clean a few times and he took them and he came back at me and hit me a couple of times himself.
"Once I started finding my range, started catching him with good shots, it didn't take me long once I caught him clean."

Entertainers Starkidz were "cornered" by the gang after a Christmas lights switch-on in Formby, Merseyside.
The performers, including one as young as 13, were abused, with one punched and another threatened with an airgun, said the troupe's manager Jan Hayes.
"We may not return to Formby next year," she said.
"We've been going for five years and we have never had any trouble like this.
"It started off with these teenagers trying take their hats or telling the children they are not real elves.
"Later on, a gang of about 20 cornered our group and one member was punched in the stomach as they were abused."
Ms Hayes said the one of the performers had an airgun held to his head.
"It was a very traumatic experience," she added. "The group member is extremely upset by this."
The elves have received dozens of messages of support via social media from parents.
One local mother, Nicola Cowie, said: "Starkidz bring so much to our community, they bring magic to life.
"Her Elves give it their all, they live and breath as elves while they're dressed in those costumes. I'd be so disgusted if my child acted they way those youths did."
A Merseyside Police spokesman said it was investigating a report of anti-social behaviour by a group of youths at the event.

Doris has been recovered, said Wrexham police inspector Paul Wycherley, who tweeted that two suspects had been arrested following a chase on foot.
Doris, Blessing and Wheely Good Sheep were painted by schoolchildren and placed on St Giles Way this month.
Website Wrexham.com said they were installed to mark the Tour of Britain cycle race being held in the area soon.
Josh Taylor says he "learned a lot about himself" in his Commonwealth super-lightweight title defence against South Africa's Warren Joubert.
[NEXT_CONCEPT]
A group of performing Christmas elves has been left "traumatised" after being attacked by a gang of teenagers.
[NEXT_CONCEPT]
Two people have been arrested after one of three newly installed sheep sculptures was stolen in Wrexham.