Suarez's departure to Barcelona for 75 million ($125 million) following his four-month ban for biting during the recent World Cup has left Rodgers with a big hole to fill.
The Uruguayan international scored 31 goals last season as Liverpool finished second in the Premier League, just missing out on their first top-flight title since 1990.
Rodgers has since added eight new players and with Sevilla full-back Alberto Moreno set to add to that number, a replacement for Suarez remains the one piece missing from the jigsaw.
"If we can add one or two more we'll have had a great window. I think this summer will be our biggest window for the next few years," Rodgers said.
"It was always the case that we needed to improve the squad. We haven't brought in another striker so far apart from Rickie Lambert.
"The money is there but there has been no panic buying. We needed to improve the squad whether Luis was still here or not. We will look to improve at the top end of the field until the very end of the window.
"If not, that means the right player hasn't been available. I'd be happy to go into the season with the squad we've got."
Liverpool lost out on the title by just two points to Manchester City last season and Rodgers hopes that near-miss will provide the platform for another attempt at ending the club's long wait to add a 19th title to their roll of honour.
"What we did last season has gone but it has given us great belief going into this year and we are looking forward to the challenge of moving the club forward," he added.
"Like all the top teams you want to win a trophy. That would be an aim for ourselves. But in the league it's about sustaining Champions League football. That means fourth place which you want to achieve and then look beyond that. We are looking to challenge and be up there again."
Schneiderlin set to feature
Liverpool will be without new signings Adam Lallana - the former Southampton captain - and Lazar Markovic against the Saints, with defenders Daniel Agger and Jon Flanagan also on the injured list.
Meanwhile, Southampton boss Ronald Koeman is entitled to feel relieved that the season is finally getting underway.
The pre-season at St Mary's has been dominated by comings and goings although, having seen a succession of key players leave - including Lallana, Rickie Lambert and Dejan Lovren to Anfield - the flow has at last been reversed.
The arrival of striker Shane Long from Hull City and Steaua Bucharest centre-back Florin Gardos in midweek took the total of new faces in Koeman's squad to eight.
The Dutchman will make a late decision on whether to involve Long at Anfield, but he insists Morgan Schneiderlin will be part of the squad, despite the midfielder pushing to be allowed to move to Tottenham Hotspur.
"He showed me that he is ready to play in the last week of training. I expect him to stay because he is not for sale,"Koeman said.
"We knew we lost some good football players but we have brought in some new good players and that showed the ambition of the team.
"We are still looking forward to bring one or two more in - we need one more in the wing position and the club is still working on that."