Lovren is encouraged by Liverpool's fine start and believes they can better last season's fourth place as they juggle challenging in the Premier League with competing in Europe.
“We always want to be better than last season," said the former Southampton stopper.
“It's difficult to predict now at the beginning of the season how things will go. But we've started the season in good shape and good form.
“Now we must continue like this and I'm confident that we can achieve at least as much this year.
“We just need to step it up a little bit against the so-called smaller teams too.
“Here you're fighting for your lives in every game, against the top team, the bottom team, against every team."