Arne Slot’s side have secured a seeded position in the Champions League last 16 after topping the league phase.
They now aim to reach Wembley later this week by hosting Tottenham in the second leg of the Carabao Cup semi-final.
“We have had a great start and everything is fine for us at the moment, even in the Champions League,” Konate was quoted in a recent Reds matchday programme.
“But I think the most important thing is that we start again and we work even harder because we’re into the second part of the season now.
“We have to work a lot because everyone wants to beat us, so we just have to keep going all the way to the end. It will be very difficult and we have to work so, so hard just to keep going and remain calm.”
The No.5 added: “Of course, this title (the Premier League) is the only one that has been missing between my hands in England (domestically)and I really hope this season we will achieve that.
“We know all our fans are behind us and we have to do everything we can to achieve this.”