Brendan Rodgers received a good luck text from Luis Suárez before Liverpool’s Premier League opener against Southampton and claimed the win could set the tone for another title challenge without the brilliant Uruguay international.

The Liverpool manager described the 2-1 win as “vital” after goals from Raheem Sterling and Daniel Sturridge compensated for a laboured display against a Southampton side showing few ill effects from the summer of upheaval at St Mary’s Stadium. Sturridge’s goal was his 36th in 50 appearances for Liverpool, a more prolific return than any player in the club’s illustrious history since George Allan in the late 19th century, and the England international believes last season’s runners-up will be stronger despite his former strike partner’s £75m move to Barcelona.

Suárez will be presented to Barcelona supporters when Luis Enrique’s team play León in the Joan Gamper Trophy on Monday, after his four-month ban from all football-related activities for biting Giorgio Chiellini at the World Cup was relaxed by the court of arbitration for sport last week. And Rodgers revealed Suárez has not severed all ties with Liverpool and was among his well-wishers for the new campaign.

“Our ambitions here at Liverpool have to be bigger than one player,” said Rodgers, when asked if Liverpool could mount a title challenge without last season’s leading goalscorer. “Luis sent me a lovely text this morning wishing us all the best, which was a great gesture. He is a friend now of Liverpool. We are bigger than any player. We do still want another striker but that will depend on the availability. Today was about winning and we got there.

“We believe in the way we work. I don’t think anyone has given us any hope of getting in the top four but that was the case last season as well. I have an inherent belief in these players. We are by no means the finished article. We are bringing in young players who are not ready-made but will improve and we will attack this season in the same way.

“We have got ambitions to be fighting and challenging. We loved the challenge of being in the title race last season and we are looking to recreate that. You do that by winning games and performing. Today we won the game and it gives us hope we can continue the great run of form we have been on for the past 18 months.”

Rodgers added Suárez’s text was sent to him personally and that he did reply. “It was a real love-in,” he said. “He’s a great boy but he is gone now.”

Sturridge, who scored 21 Premier League goals to Suárez’s 31 last season, struck in the 79th minute to give Liverpool victory and believes the team can improve this term. “There is pressure on myself to get the goals with Luis Suárez out of the team,” he said. “It’s important for myself and the lads to step up and it’s important as a collective unit that we score the goals. Are we stronger this season? I think so. No disrespect to Luis. He’s a great player and will be missed. But we move on. We have proved we can win games and score goals.”

Simon Mignolet produced a superb save to deny Morgan Schneiderlin with two minutes remaining and preserve three points for Liverpool, and their manager insisted performances will improve once players recover from a disrupted summer. Rodgers said: “Most clubs’ pre-seasons have been broken with players coming back late. We had to grind out a result. This was a brilliant win for us. It was a tough game. As the season rolls on we will get better and more fluent.

“Southampton are a good side with a good manager. Just because they have lost players doesn’t mean this was going to be a walkover. To get the three points was vital. The first win can really set the tone for the season.”

Ronald Koeman lamented Southampton’s failure to add a second goal during a dominant spell in the second half and insisted defeat was harsh on his new-look side. The Dutch coach said: “At 1-1 I think there was only one team on the pitch playing and that was Southampton. We did everything except scoring in the second half. We created two great possibilities but the quality of Liverpool is that they don’t need a lot of opportunities to score two goals. If we play that way and keep that team spirit I don’t think we will struggle at all this season.”