Tonga coach Kristian Woolf called the 30-12 win over England special, but said his side still had work to do at the World Cup.
"It's is a good position. We came here to win, and we knew the importance of the game," Woolf said.
"It's a big thing to get up and beat tier-one nations, and it's only happened a few times ... so really proud of the group. It's really special.
"But we've got to go and get a job done against Lebanon, and then we know we've got a big game the following week against Samoa."
Tonga, ranked fifth in the world, face No.23 Lebanon and No.4 Samoa in their final group matches. Five-eighth Latu Fainu suffered a pectoral injury 16 minutes into Saturday's game.
England, ranked third, are close to elimination after losing by four tries to two in Perth. Coach Brian McDermott was in charge for the first time.
Only two teams from Pools B and C advance, making England's path dependent on results elsewhere and points difference.
If Samoa beat Tonga and avoid defeat to Papua New Guinea, Tonga would likely advance over England on their head-to-head win. If Tonga beat Samoa, England and Samoa could finish level on two wins, with points difference likely deciding the other semi-final place.
Samoa's 78-4 win over France gives them a substantial advantage. England play France and Papua New Guinea over the next fortnight, but McDermott warned against assuming they could simply score heavily.
"We're not going to trip ourselves up trying to come up with a plan about scoring 50 points next week," McDermott said.
"It would be tremendously disrespectful to either France or PNG to suggest that we're going to rack a load of points up."
He also rejected the idea of playing without restraint, stressing possession and ball control.
"You can't play with freedom - not at international level," McDermott said.
"You've got to keep hold of the ball. Trying to get fatigue into the opposition is a hard thing if you're dropping the ball like we did.
"I saw enough against Tonga to tell me that we're heading in the right direction."