It was his first competitive strike for the Reds, having notched four times for the club in pre-season after arriving from Celta Vigo in the summer.
Rodgers said, "The goal was important for Iago's confidence. It has been difficult for him.
"You've got a world-class striker [Luis Suarez] playing week-in, week-out, getting goals, and then you've got Daniel Sturridge supporting.
"So he's been the cover player a lot of this season, apart from the opening period. It was good for him to get his goal in front of the Kop and hopefully that will give him a lot of confidence.
"[The whole squad] has to contribute; you can't rely on 11 or 12 players. Brad Jones coming in was excellent - he has been a really loyal No.2. He didn't have much to do today, but in what he did do his hands were clean and his distribution was very good."
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