Thomas Tuchel's side were far from their best as they edged past DR Congo, needing two late goals from captain Harry Kane to progress to the round of 16.
Rooney did not hold back with his assessment of the performance after full-time.
"For me there are big concerns. We are all delighted England have gone through but in particular when England lose the ball they are so open," Rooney told the BBC. "Against a better team I think we are in big trouble if we don't sort that out.
"The connection isn't great between the backline and midfield, the full-backs are struggling, Madueke struggled. There are just no connections and big gaps in the middle of the pitch and that is a big worry for me.
"He really needs to look at that otherwise we will go out."
England beat DR Congo on Wednesday but struggled for large parts of the match, and will now face Mexico in Mexico City on Monday morning.
Rooney also suggested England should have called on the experience of Kyle Walker following an injury to Tino Livramento.
"We've seen it before where players have come out of retirement... I think the minute Tino Livramento got injured, they should have been straight on the phone to Kyle Walker," Rooney said.
"Kyle's still more than good enough and more than capable of playing in this England team. I would have been on the phone to him and saying, 'Listen, we need you here so can you come out and help us', because that could really cost us. I'm worried on that."
Rooney was also critical of Djed Spence's performance at right-back.
Despite his concerns, Rooney reserved special praise for matchwinner Kane, who has now scored 13 World Cup goals.
"His header was brilliant but the second goal was incredible and he is just such a top player," Rooney said. "All the best players in the world are performing at this World Cup, he is England's superstar, he is the hero for us.
"There are few things that they need to clear up: I wasn't too sure about midfield and defence in that performance but the main thing in football is you get through and Harry Kane has done it again for us."