The Reds were able to secure a top-four finish last season, with 19 games negotiated at Anfield without defeat.
While such an unbeaten run is to be applauded, Jurgen Klopp’s side were held seven times in front of their own supporters.
Redknapp has warned that number will have to be cut considerably if a challenge is to be sustained for the top-flight crown, with Liverpool placing too much emphasis on entertaining at times.
The former Reds midfielder told Sky Sports on the back of a summer which has raised expectations on Merseyside: “Manchester City are the outstanding favourites still, of course. They're a fantastic side and I feel like they will still come out on top. But Liverpool are in contention.
“There's a lot of talk about them having to make up a 25-point deficit on Man City from last year but remember Man City had to make up a big deficit on Chelsea from the season before. The challenge for Liverpool will be ensuring they don't throw away points needlessly.
“Loris Karius has obviously received a lot of criticism - and Alisson will improve them - but you can't hold the goalkeeper accountable for 0-0 draws at home to the likes of Stoke and West Brom, who both went on to be relegated.
“They had seven draws at home last season and they need to find a way to edge those close games if they are really going to push City.
“At times Liverpool play such good football and it feels like they're looking for the perfect goal - but often it's the ugly goals that are the crucial ones, earning you those scruffy three points when you haven't been on top form.”
Liverpool opened their 2018-19 campaign with a convincing 4-0 victory over West Ham on home soil.
Their next outing will see them head to Crystal Palace on Monday, with Redknapp looking forward to seeing how the Reds manage a star-studded squad through a gruelling campaign.
He added: “Klopp will just need to maintain that happy balance in the squad. It's one of the challenges of having talented players on the bench. Yes, it's all smiles at the start of the season but after 25 games that good feeling wears off a little bit if you've been sat on the bench for most of the time.
“That was something Pep Guardiola did well at City last year, keeping all of his squad happy and feeling involved in the success.
“Football is about squads these days and you need everyone ready to step in when required.”