Elliott scored in the 4-2 win on Sunday.
Sturridge said: "I had a chat with Harvey Elliott a few weeks ago and I told him to shoot more. For me has the ability to do it and I think as a younger player you might shy away from it with Mo Salah, Darwin Nunez and the pressure to feed them.
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"In this day and age you want flexible players.
"He can play on the right for a few games, on the left and in the middle which will help him to play consistently for Liverpool."