The Anfield skipper first offered the job to Jamie Carragher - but the defender, 35, turned down his early retirement present.
Sturridge added: "Stevie was very nice to let me have the penalty.
"I guess he knew my pain and thought he would be kind to me.
"Before that, the keeper made some good saves when I was hitting the target. When you hit the target and the keeper saves it, there is nothing you can really do. The keeper did his job, I was doing my job - he got the better of me."