Jurgen Klopp’s men overcame a late scare to secure the win. In the 87th minute, Johann Berg Gudmundsson equalised Mane’s stunning opener but a late header by defender Ragnar Klavan ensured the Reds left Turf Moor with the maximum points.
“I think it is not our best game but I think we deserved to win because we created many chances and we got two goals," Mane told club website.
"We have some important players missing today. But we have other players and we can count on them and they do well.
"But more important we are a great team, great club and that means we are on a good way. Everybody is working hard so we deserved to win."
The New Year Day win over the Clarets saw Liverpool make it three wins and one draw from their last four fixtures. And Mane who sees nothing special in the feat wants more consistency in their performance.
"Honestly I think this is what we can do because we try our best and try to win [as many] games as we can. To get 10 points out of 12 I think is great.
"I think this season is too early to talk about [the table]. I think more important for us is keep [going] game by game and try to win and we are going to know the table at the end of the season."
Meanwhile, Klopp has confirmed that the Senegal winger, alongside club teammate and Egypt international Mohamed Salah will make the trip to Accra, Ghana as both players - with Gabon's Pierre-Emerick Aubameyang - slug it out for the 2017 Caf African Player of the Year title.
The Awards Gala takes place on Thursday and the duo will be expected back in England in time for weekend's crucial cup clash.