Pep Guardiola has urged Raheem Sterling to step up in the absence of Kevin De Bruyne, with Manchester City fearing the Belgium playmaker could be out for nearly a month because of a hamstring injury.

De Bruyne limped out of City’s sixth successive Premier League victory under Guardiola on Saturday – a 3-1 win at Swansea City – after sustaining the problem. The manager admitted afterwards that the prognosis did not look good, with medical staff due to assess his condition on Sunday.

However, while the player was initially optimistic he had suffered only a minor strain and would be sidelined for a couple of weeks, it is understood that the injury is a minor tear and he is likely to be out for up to a month. City are not expecting to have a full prognosis of De Bruyne’s hamstring problem for at least the next 48 hours, although if a tear is confirmed it would rule him out of Wednesday’s Champions League tie at Celtic, Sunday’s top-of-the-table match at Tottenham Hotspur and the fixture against Everton after the international break, with the Champions League game against Barcelona on 19 October pencilled in for his return.

Guardiola admitted his absence will be a blow but believes Sterling – who scored his fourth Premier League goal of the season on Saturday – can fill the breach.

“Kevin is not going to play the next games and now we need to keep going and win the games without him. We have to do that,” he said. “Raheem feels that. He feels that his team-mates appreciate his efforts – the staff, the coaches – we are so happy about what he has. But again this is only September. I would like to be in May with one game left but we are in September and we have only played six games. We have a lot of games to play.”

Sterling was criticised for his performances at Euro 2016 after a disappointing campaign that ended with England being eliminated by Iceland in the last 16. Yet the player who cost £49m from Liverpool acknowledged that the arrival of Guardiola, the former Barcelona and Bayern Munich manager, in the summer has helped to transform his approach.

“The manager has told me to enjoy scoring goals and seeing the ball go into the back of the net. He gives everyone the confidence, not just me,” Sterling said.

“He gives everyone the belief and the motivation. His speech before [the game] was fantastic and it means that when you go out on to the pitch you are really fired up for the game. This is a team that is forever growing and developing. Those relationships are developing, the team spirit is great in the dressing room, on the pitch, we are fighting for each other and we need to keep that going. We are trying to improve and not relax, that is what the manager is trying to get us to do.”

He added: “I have had a few chances over the last couple of years and I need to be finishing them off. What is going to make me the player I want to be is scoring more goals, being cool in front of goal and scoring as many as I can.”

City will visit Celtic aiming to achieve an 11th successive victory in all competitions under Guardiola. Sterling will come up against Brendan Rodgers, who gave him his full Premier League debut at Liverpool in 2012, and he admitted his former manager has played a crucial role in his development.

“He was massive for me. I try to learn from every manager I work with and he is a man I definitely learned a lot from,” Sterling said. “When he first moved from Liverpool I spoke to him then and have spoken to him a couple of times since. I have changed my number a couple of times since then, so I look forward to catching up with him and hopefully getting his new number.

“He is a fantastic guy. He played me in different positions to help me understand those roles and what it took. He gave me a lot of confidence. It will be good to see him again and I wish him well – but on the day it all comes down to winning the game.”