The England striker did not look lost without him on Sunday, though, as he and Sterling both scored in a 2-1 victory over Saints.
"It's important as a collective unit that we all provide the goals, but it doesn't matter how many we get so long as we defend well and get the goals we need," Sturridge told Sky Sports 1.
"I think with ourselves and the other boys, especially the ones the manager has brought in, with myself and Raheem we have a connection. We go out there and have a laugh and a joke on the training field, but we go on the pitch and give each other abuse at times but we like to get the best out of each other.
"I'm the older brother so I give him more stick than he gives me!"
Their goals came either side of a Nathaniel Clyne equaliser, and Sturridge's in particular eased the nerves after the unfancied visitors came on strong.
"The first game is always difficult," Sturridge added. "The pace was high, we worked hard and controlled things, but when they got a goal it was difficult for us.
"But we got the result and that's what matters."
Asked if Liverpool were stronger without Suarez, Sturridge added: "I think so, with the players we have brought in. No disrespect to Luis - he's a great player and he'll be missed - but we move on from that.
"We have shown we can win games, score goals and defend as well. But with the little man (Sterling) and the other players producing the goods, we'll be okay."
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