Jovanovic has arrived on a Bosman from Standard Liege.
He told LFC Weekly: "My main thing now is to show Roy Hodgson that the club hasn't made an error in bringing me here.
"The coach is fantastic. He speaks very openly with us and tries to put across his ideas clearly. I hope that I will learn more and more. I accept the coach's words and now it is up to me to show him I really can do everything he asks me to do.
"I have only been here a short time but I want to show all my qualities.
"I know that physically the Barclays Premier League is a demanding league but when I thought about this characteristic, I thought: 'this is me'.
"I think I can do everything I need to play at the top level here. It is a long season and if you count games with the national team as well, you can be looking at 60 or 70 games but I feel okay and of course I am really looking forward to it.
"I couldn't have asked for more from the other players in making me feel welcome. They have been very kind and I feel very close to the group in a short space of time.
"I am 29 and feel I am at my best. I feel this is my best time and I am with the best team."