England star Farrell, who won the second Test in Wellington with a 77th-minute penalty, left it 60 seconds later this time as the British and Irish Lions claimed a 15-15 draw.
It meant the series finished 1-1, and leaves the 1971 Lions remaining as the only squad ever to have won a Test series on New Zealand soil.
"It's a bit weird, really," said Farrell, who booted four penalties, while wing Elliot Daly landed a long-range effort as the Lions fought back after conceding first-half tries to Ngani Laumape and Jordie Barrett.
"I suppose it is a brilliant achievement. At the same time, it is never nice to be on the end of a draw.
"It was another tough and proper Test match. It has been a brilliant series.
"This is a fantastic team we were playing against.
"Ours was put together not so long ago, and it shows the quality of players that have been picked to have such little preparation and be able to not just compete, but properly be up there and feel like we could have done better."
Farrell played down his match-levelling exploits, but once again the Saracens marksman's goalkicking withstood fierce pressure as he recovered from a hesitant overall performance, especially during the opening 40 minutes.
"I had been hitting them okay, so I was happy," he added. "I was wondering whether a bit of wind could have picked up. It was a long kick, but I was just trying to strike it well.
"You know what the kick means, but I don't think anything changes for you as a kicker. All you do is try to stick to hopefully what you have done well before that."
The Lions will return home on Tuesday, having surpassed most expectations of what they might achieve on All Blacks' territory, even if Test series glory eluded them.
"Playing against them (New Zealand), you have to stay on it," Farrell said. "The next job has to be a good thing, because if you don't and you let them out of their half or you let them into your half, you can get punished for it.
"Whatever you are doing next is obviously important, but they are obviously a very clinical side and you have to try to keep the pressure on them, which we have done at times and not done at times.
"You want to play the best team, don't you? And they are number one in the world. Everybody wants to play the best team, so this is no different.
"You obviously learn from playing against them. You learn from playing in any big game like this, and especially a Test series when you play them three times.
"Everybody wants a go at the team that's top of the log.
"It has been an unbelievable tour. I think everybody has thoroughly enjoyed it.
"We always thought we would be competitive - I don't know what everybody else thought. We came here to win. We have always said that.
"There are some good players here, high-quality players, and when you start learning from each other and pushing each other, then you start putting performances together. And you see that later on in the tour."
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