The Reds narrowly missed out on the top-flight crown to Manchester City last season, and were forced to sell Suarez to Barcelona in the summer after his excellent campaign.
Redknapp believes that the Uruguayan's departure, along with the addition of several new players taking time to settle in England, will stop Brendan Rodgers's side from competing for the title.
He told reporters: "I thought they were great last year. When they beat Man City I was sure they would win the league, then Chelsea went there and did a job on them and it took it away from them. I thought overall they deserved to win it last year.
"They have lost the fourth best player in the world in Suarez and it is difficult to replace him but they have got lots of good players there. Again, they are bedding in new players and it takes time.
"They will be there pushing for a Champions League place again this year I'm sure - I don't see them winning the league this year."
QPR face Liverpool in their Premier League clash on Sunday.