The midfielder signed for Aston Villa last month in a loan deal with an option to buy for £35m.
Elliott concedes it was difficult leaving Anfield, but felt it was the right decision at this stage in his career.
“It was very difficult,” Elliott said. “First of all the decision to leave and then on top of that to find the best club. There were a few difficult decisions I had to make.
“I had to sit down and speak to the team and go into a lot of detail, but it was the decision that was made and the decision was to come here.
“I’m over the moon. As I said in my first interview, I’m so happy to be here and I really want to kick on, to get this club where they deserve to be. With this team, anything is possible and we just need to fight together and keep going.”
“I loved every minute of it; every second, every day,” Elliott reflected on his time at Liverpool. “I wouldn’t change it to be honest, I learned so much from being there and experienced many things.
“But I think the most important thing for me when I was making the decision was to be playing first-team football. I need to be in a team where I’m getting regular minutes. Whether that’s starting or coming off the bench, just having that feeling of going into a matchday knowing you’re going to play, that’s the only way I can improve now.
“The love I have for Liverpool is still going to be there forever, that’s not going to change, I’m still going to be watching and looking out for them from afar. I’m wishing them all the very best.
“But sometimes in football you need to be selfish. I made the decision to leave because I wanted to do what’s best for me. I take all of my experiences and everything I learnt from Liverpool. Hopefully I can start to kick on now.”