Liverpool have started the season off strong in their bid to capture the Premier League crown, with Jürgen Klopp's side winning their first six matches.
"It was a good goal, the boys worked tirelessly all game", Sturridge told BT Sport postmatch.
"My cousin gave me some stick the other day for celebrating against Chelsea because he's a Chelsea fan; I think in the moment like the other night I got excited and celebrated".
"I'd like to think [I've scored better goals], but probably not".
"I think City and Liverpool are a step forward of us, but I think also we are more close than I thought one week ago", said the Italian.
Daniel Sturridge's well-documented injury concerns over the last few seasons have left his Liverpool career in a permanent state of uncertainty.
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It was his 50th Premier League goal for Liverpool and kept them unbeaten in the league this season, level with Manchester City on 19 points at the top of the table. "It's all good with the result".
At the start of this current campaign, Hazard has hit the net for Chelsea seven times providing two assists.
"I think he's a top, top player". But coming into a game like this, constantly in [potentially scoring] situations, that makes him a world-class player.
"It's like riding a bike and it's not that you wake up in the morning and can not ride a bike anymore". "The boys worked tirelessly all game, we created chances in the first half and we were unlucky not to score". It is not like you wake up in the morning and you can not finish any more, or you can not ride a bike anymore.
Chelsea now sits third in the Premier League, sporting a 5-0-1 record following a scoreless tie against West Ham on September 23 that ended its flawless run.