The defending champions will now face South Africa in the semi-finals, after crushing hapless France with a nine-try thumping.
Savea took his staggering Test try tally to 38 from 39 caps, overtaking Lomu's career total of 37, and Mike Umaga's haul of 36.
"I've always said that no one can come close to Jonah, he's amazing," said Savea.
"I wouldn't say it's pressure to have comparisons.
"I watched him in every home game in Wellington running over people like little kids.
"It's awesome to be compared to him and it's an honour but I'm just doing my job as best I can."
New Zealand boss Steve Hansen confirmed prop Wyatt Crockett suffered a groin issue that will be assessed on Sunday.
Wing Nehe Milner-Skudder picked up a shoulder problem, and both will be early doubts for the South Africa semi-final.
New Zealand have already lost loosehead prop Tony Woodcock to injury for the tournament, with his replacement Joe Moody completing the brunt of the France clash after Crockett suffered his groin problem.
Savea's savaging of France will doubtless strike fear into all opponents, as New Zealand cranked up their World Cup tempo.
The All Blacks came alive when it mattered most, to a man delivering on a performance of gusto, guts and guile.
Savea equalled Lomu and Springbok flyer Bryan Habana's joint record of eight tries at a single World Cup tournament.
Habana - tied on 15 tries for the all-time World Cup scoring record with Lomu - tweeted Savea to congratulate the 25-year-old on matching his mark.
"I've always watched him since I was a youngster," said Savea of Habana.
"And he's a legend in my eyes really.
"And I guess to have that accolade is pretty awesome.
"South Africa played well too, so we'll enjoy the moment but refocus pretty quickly.
"It's awesome to be a part of this occasion, it's a huge privilege and honour for me and my family just to be a part of this team.
"I can't say how special it is to me. I think everyone was on fire. The whole team was in one sync, I was really proud of the boys.
"From the first whistle to the last it was an outstanding performance.
"I was eager to get to the try-line no matter what, it's about being hungry to get there no matter the obstacles.
"I wouldn't be able to do what I do without the forwards giving us great ball. There's always improvement, and that's what gets us excited.
"Knowing we can improve next week, that's an eye-opener really."