The Irish ruthlessly took their chances in the 36-14 win over Scotland to set up a last-eight meeting with three-time champions New Zealand back at Stade de France next weekend.
"I don't think and neither does the team think that we have played our best rugby," Farrell said. "We know where we want to go and what we want to achieve.
"Will we ever get there? I don't know. But it's days like next week that are coming where we need to find out a bit more about ourselves and these lads are more than willing to do that."
Ireland, who have never won a knockout match at a World Cup, dismantled a Scottish side also looking to advance to the knockout stages, scoring early and scoring often to extend their winning streak to 17 straight games.
They had to get through a period of sustained pressure from the Scots after their first try, however, and Farrell thought the way they held firm then struck back at the other end was the key to the match.
"When you see how we were clinical and add how we were defending, it is a shot in the arm for us and a hammer blow for the other team," Farrell said.
There were a few injuries to concern Farrell, however, with wingers Mack Hansen and James Lowe forced off the pitch and lock James Ryan needing attention.
"Mack went off with a HIA (head injury assessment) and felt his calf straight away so we got him off," he said. "James Ryan has a bit of a knock on his wrist that we need to assess more, so we will see how he is.
"James Lowe got a bang in the eye, it shut and he couldn't see much, his vision was coming back towards the end of the game, which is good."
The crowd of vocal Irish supporters outnumbered the Scottish fans considerably, creating a raucous atmosphere as they had at the same stadium when Ireland beat South Africa earlier in the pool stage.
"We play for them, I was talking about it earlier when we were in the dressing room," Farrell said.
"It's more important than people think. When we get back to training on Monday, we'll be doing it for them."