The Senegalese winger was in fine form once more, firing the goal to put the Reds 3-0 up at half-time following Adam Lallana's breakthrough and a well-taken James Milner penalty.
Philippe Coutinho immediately cancelled out a strike from Hull's David Meyler with a trademark 25-yard curler into the top corner, before Milner scored from the spot again to mark the first time Liverpool had scored five goals in one league game at Anfield since February 2014.
But though Jürgen Klopp's men have supporters daring to dream of another title challenge, such is the impact of their devastating array of talent in the final third, Mane insists they mustn't get carried away.
"We must take it game-by-game" warns winger
Mane told reporters afterwards that they "played really well" in the first-half to be in "a great position" at half-time, insisting that they "continued to do our best in the second-half" and "could have had more goals."
The 24-year-old insisted that the "most important thing" is that Liverpool "kept this run going" for their fourth straight win in all competitions and their third successive league triumph, adding: "We didn't stop. We kept pushing until the end."
Mane, who netted his third of the season with a precise finish into the bottom corner, said he was "pleased to score" and hailed it as "great" for his confidence, though he insists he was "happier" with "the fact we got the three points."
On the ambitions of this Liverpool team, the forward declared: "It's just the beginning of the season. It's too early to think about what this team can achieve."
Instead, Mane said Klopp's charges must "take it game-by-game" because they are "in a good way" collectively and need to "just keep working hard" and to "try to keep this winning run going."
Mane delighted with Liverpool's "great football"
The £30 million summer signing has yet to taste defeat as a Liverpool player, having been out injured for their only reverse so far this season, and produced another influential performance on L4.
Mane didn't have as direct an impact as Coutinho and Lallana, with their one goal and two assists respectively, but helped set the tone for the evening with another lively display as he continues to quash the concerns over his consistency which followed him to Merseyside when he joined in July.
He declared himself "very happy" as he spoke about his career having gone "so well" since signing for Liverpool, which he called "one of the biggest clubs in the world" and said the entire squad "all want to bring success to this club."
"We are playing some great football," insisted Mane, who also spoke about how his teammates are "working really hard both with and without the ball."
The wide-man said that there are "always players around for you to link-up with" on the attack, such is Liverpool's willingness to get forward, and said that even when they don't have possession they "all try to get it back quickly" and "try to help each other on the pitch."
Mane vowed that Liverpool will "try to keep going" and said that having Klopp on the touchline is "great" because he is "always communicating with us [the players] and encouraging us" and "pushes us on."
Mane: Anfield form will be "different" this season
Liverpool are now unbeaten in their last 10 league games on home soil, a run which has seen Manchester City, Everton, Chelsea and champions Leicester City all visit Anfield.
This victory, in addition to a similarly commanding win against Leicester last time out, also means they have scored four or more goals in their opening two home games for the first time since 1959.
Mane hopes that their performance levels in front of their own fans can establish a strong headquarters for Liverpool, who claimed just eight wins from 18 on home turf last term.
He said that this season "will be different" for the club at home and that they have "shown what we can do" and their hopes of making Anfield "a really strong place."
Mane suggested that the atmosphere of their home stadium helps spur on the team "to play better" because they have "some of the best fans in the world" and have received support which has helped them "to become better and better" against Leicester and Hull.
"We have amazing fans and we want to give something back to them," added the Reds' No.19, who lauded Anfield as "a great place to play football."
He also talked of the team playing "with a lot of confidence" which comes from "winning games" and hinted that if they can continue their home form then the fans "will really push us on this season."