The Irish province won with a try for flanker Niall Ronan and four penalties from Ronan O'Gara on his 100th Heineken appearance.
"It was a really hard-fought win," said O'Connell. "We started really poorly and when you start like that against a team like the Scarlets, with the calibre of player they have, you get punished and that's what happened.
"They scored an early try and a penalty and we were probably lucky they missed two kicks at goal, but we settled down then."
The result leaves Munster top of Pool 1 at the midway stage, ahead of next weekend's return meeting.
"It's a hell of a win for us and we are absolutely thrilled with it, but we are fully aware it's only half-time," O'Connell added. "From our point of view there is nothing like a loss to focus the mind so I'd imagine next week will be an incredibly tough game.
"It's a great win and we are very proud of it.
"I thought our pack was excellent. We got a lot of yardage from our scrum and some points from our scrum.
"It's massively important we have got a home game next but it's not like we are running away with any games. Every game is a fight to the death at the moment and every game is a battle.
"There is no danger of us getting ahead of ourselves. We know how close the games are and we will be fully focused against the Scarlets next week."
Scarlets head coach Nigel Davies rued his side's failure to take their chances as they were forced to settle for a losing bonus point after seeing their 100% record in Pool 1 evaporate.
"We weren't accurate enough and we had a couple of chances in the first 20 minutes we weren't sharp enough at taking, and we left eight points place-kicking-wise and you can't afford to do that against Munster," said Davies.
"We were very confident but we weren't accurate enough. This match was of Test-level intensity and you can't afford errors but there were too many in our game.
"But we have always seen this as a two-match series and we have to go out there (to Ireland) and get something from the game.
"It's a tough place to go but we will go there all guns blazing as we did against Northampton.
"We have got the team to beat them. We will go out there and give it a crack but we have to be sharper and more accurate."
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