Suarez starred for Liverpool last term, scoring a stunning 31 goals in 33 Premier League appearances as the Anfield giants came close to winning their first title for 24 years.
The Uruguay forward moved to Barcelona for a reported fee of £75 million last month, though, and his absence means Sturridge - who himself scored 21 top-flight goals last season - will be tasked to lead the Liverpool line in 2014-15.
Brendan Rodgers has wasted little time in spending the Suarez money, and more, as he aims to bolster his squad, with the likes of Adam Lallana, Dejan Lovren and Lazar Markovic headlining their close-season arrivals.
And Sturridge - scorer of the late winner in their 2-1 win over Southampton on Sunday - feels Liverpool's squad is more well-rounded this season.
When asked if this year's group of players were stronger, Sturridge told Sky Sports: "I think so. With no disrespect to Luis, he's a great player and he'll be missed.
"But we can win games, score goals. We were just unlucky to concede the goal [today].
"I think, of course, there's pressure for me to get the goals now, with Luis out of the team.
"He scored 30-odd goals last season. It's important, not just for myself, but for the other lads to step up now.
"It's important that as a collective unit that we all provide the goals. As long as we score goals and defend well, we'll get the results that we need."
Liverpool were not at their best against a Southampton side, who, despite being decimated by a spate of sales in the close-season, had chances to win the game.
Nathaniel Clyne's 56th-minute effort cancelled out Raheem Sterling's well-taken opener and Steven Davis had a great chance to give the visitors the lead in the final 25 minutes.
He fluffed the opportunity, though, allowing Sturridge to be the hero when he poked home from four yards after reacting to Sterling's header fastest with 11 minutes remaining.
"They made us work very hard for that," Sturridge conceded.
"First games are always difficult and the pace of the game was high. We worked hard, we probed. When they got the goal it was difficult for us but in the end we got the result."
Man of the match Sterling echoed his team-mate's view, adding: "It's definitely good to get off to a good start. They made us work really hard but the boys grinded through and luckily we got the goal through Daniel."
