The Welsh midfielder moved to Anfield from Swansea City for a reported £15m and believes that his confidence will help him be a success at his new club.
Allen said: "You aspire to play at the highest levels and be the best player you can, and these are obviously the things that come with it.
"You have to have massive belief, it has to border on arrogance at times. I think you can see the difference of a top player playing with belief or without it. That's something you have to cope with in football and something we strive to achieve.
"I said to myself that I'm going to approach this year the same as I've approached any other in my football career and give it everything I can, and at the end of the day say to myself, 'Have you given your best?' If you have, you can't do any more than that."
Allen is expected to start for Wales in the World Cup qualifying match against Belgium on Friday.