The 22-year-old followed the Northern Irishman into Anfield from Swansea this summer, completing a £15 million move after representing Team GB at the Olympic Games.
And Allen has backed his 39-year-old boss to turn the Reds around, stating his motivational skills will give the players confidence.
"He is a manager who instils faith and confidence in you," Allen told the Daily Mail.
"It really makes a difference and helps when you go out on to the pitch. I’m sure the other players here will find that out soon.
"I think they are all looking forward to it as much as me. The manager he is passionate about football. His heart will be in this job 24/7.
"Individually and collectively, he will give every player what they need to go out on that pitch and perform."
The Wales international was also keen to play down comparisons with Barcelona duo Xavi and Iniesta - whose pass completion rates he bettered during the Swans' maiden Premier League campaign.
"You can read stats how you like," he continued.
"It’s great personally to hear those things; to be associated with those players is a dream. Xavi and Iniesta are two players I admire massively. They really inspired me to play a similar sort of football.
|21/10||Liverpool are 21/10 to finish in the top four with Paddy Power|
"I was even slimmer and smaller then. When I was younger coming through it was a big issue for some people.
"I was always confident there were other aspects of my game that were better off because of my size. But there were a few doubters.
"I’ve been lucky every manager I’ve played under at Swansea has been someone who has played the style of football that suits me down to the ground."
Allen went on to hail the guidance of recently deceased former Wales boss Gary Speed, who handed him his first Under-21 international cap.
"He was very influential," he continued.
"He was a great man who is sadly missed by everyone. In the year before his tragic death he was massive for me. If there are times when there are any doubts, you remember back and you realise that you’re not [doing] too bad.
"I’m ambitious. I’ve always dreamed about playing at this level of football and I have worked every day of my life to try and get here. I’m someone who wants to be the best I can be every single day."