The 24-year old striker seized on an errant pass from former teammate Jonjo Shelvey to level in the fourth minute after the Swans midfielder had struck two minutes earlier.
The goal was Sturridge's fourth in four league outings and six in five matches this season but it wasn't enough for the Reds as Michu netted from a Shelvey pass in the 64th minute after the ex-Anfield man had also gifted Victor Moses the a go-ahead goal in the first half.
"I just anticipated he would probably knock it back," Sturridge told Sky Sports of his goal.
"Sometimes it works for you, sometimes it doesn't. This time, for me, I was lucky enough that he passed it and I could take advantage."
Of the result, he added: "I think, in the end, we're a little disappointed because we were winning the game and were in control of the game.
"We conceded a goal which is obviously disappointing for us, but we showed character not to lose the game, and we almost won it at the end.
"We're back to the top of the league and we'll push on to the next game now."