But Steven Gerrard's side responded in kind on Sunday, producing a ruthless display of their own as Hibs were thrashed 6-1 at Ibrox.
Hat-trick hero Defoe admitted after the match that the scoring exploits of their Old Firm rivals has not gone unnoticed.
Asked if Rangers felt under pressure to hit the goal trail after seeing what Neil Lennon's team had produced so far, he said: 'Of course, yes. 'You can't ignore it - the way they've started and the amount of goals they've scored. 'It's nice that we've won the game so convincingly today. You don't always have to score six or seven goals. It doesn't really matter. It's about getting three points. 'But it is nice to win in that way.
'It's good for the fans as well as well as the new lads who've come in - to get goals and assists. It's good for the confidence. We just want it to continue for as long as possible.'
Defoe tucked home with his right foot, left foot and head to complete the perfect treble against Paul Heckingbottom's team.
He made way with 14 minutes left and strike rival Alfredo Morelos promptly scored twice after taking over.
But Defoe insists he will not throw the toys out of the pram is he does not keep his place for Thursday's Europa League second leg against Midtjylland.
'Would I be disappointed not to start the next game? Maybe when I was younger,' the 36-year-old said. 'Of course you want to play as many games as you can but the manager is smart enough to know the senior lads - and I don't say 'older lads' - have to be managed.
'It's important so you can put in those performances. 'It's nice to get my first hat-trick for the club. Right foot, left foot, header - a perfect hat-trick.
'It's a big day when I score a header. My last one was at Sunderland in the cup three years ago. There's been a few braces in there, though.
'As a forward it's always nice to score hat-tricks and I've always liked keeping the match ball from day one.
'It's my first one here and hopefully I can get more. I don't think I've done the perfect hat-trick before. I can't remember - it's been so long! 'It's an amazing feeling, the best in the world to get three goals and the three points.'