The Reds narrowly missed out on the Premier League title last season but are back in Europe's elite club competition for the first time in four years and begin their campaign at home to Bulgarian outsiders Ludogorets in two weeks' time.
Gerrard, 34, who famously lifted the trophy in Istanbul in 2005, told American network ABC: "When you watch the Champions League and you're not involved there's jealousy and envy seeing other players play on the big stage and hearing that Champions League music.
"You are competing against the best players in Europe and it is the number one competition in the world to play in.
"It is the trophy every player dreams of winning and because of the experience I have gained over the years I was so desperate to taste it again, even if it was just one more time."
The midfielder recently retired from England duty and is enthusiastic over the chances of helping Liverpool continue their improvement under manager Brendan Rodgers.
He said: "Without getting too carried away I think we are now a very good team and I think we can become excellent as there is still room for improvement.
"The rule at Liverpool is quite clear. You try to win every competition you enter. He (Rodgers) has been here for two years and I think he is desperate to get a trophy in the cabinet - that is goal number one.
"It is very important we maintain our place in the Champions League but after the journey we went on last year and the confidence we gained from it I think we are genuine title contenders as we have proved we can mix it with anyone in this league."