Gerrard overtook Smith in the number of all-time appearances in the Reds' 3-1 win against Crystal Palace last week.
The Liverpool skipper celebrated his 639th run out with a goal from the penalty spot, and Smith praised the midfielder in his Liverpool Echo column.
"I watched Stevie make his 639th appearance against Crystal Palace last weekend, moving him up to seventh, and I don't mind losing my slot to a player I consider to be one of the best I've ever seen in a red shirt," he wrote.
"I've been privileged enough to play alongside Billy Liddell and Kenny Dalglish, while I've seen a few hundred of Steven's performances first hand – and you honestly can't separate them.
"Gerrard passed one of my proudest milestones last weekend – and I couldn't have been happier."
The Reds are currently second in the Premier League.