The Manchester United striker has come under some scrutiny since England's 2-1 defeat against Italy in their World Cup opener on Saturday.
Despite providing the assist for Daniel Sturridge to score with an inch-perfect cross and being played out of position on the left wing, Rooney was criticised after a largely indifferent display and continuing his record of firing blanks at the world's biggest competition.
Roy Hodgson, the England manager, defended Rooney immediately after the game, but the 28-year-old has continued to be a hot topic of conversation among fans and the media. Veteran Lampard, an unused substitute in Manaus, admitted his frustration at much of the focus centring on just one player.
"Unfortunately we do have a fixation with one player during every World Cup, ones that I've been involved in," he said. "It's a bit frustrating when you're in a team group and that happens because we're there trying to play together - people are not selfish in this squad - trying to get results and a fixation with one player can become, rather than a debate, a bit of an agenda.
"So I do think we need to drop the agenda and look at the team, whoever plays, because the manager will pick the best team that he sees fit and whoever plays we want to win."
Lampard believes Hodgson's men can take heart from their performance against the Azzurri, but knows that it will count for nothing unless they win against Uruguay tomorrow and then Costa Rica next week. "I thought we started very bright, some good attacking football, there were a lot of positives out of the game, the one negative was that we didn't win it," he said.
"Importantly now [we must] look forward, take those good points, try and keep them going and improve on them. We need to win games."
Several youngsters came to the fore over the weekend and Lampard hailed the likes of Raheem Sterling, Sturridge and Ross Barkley as a breath of fresh air.
"[They have had] a big impact. From the minute the manager picked the squad I think we were all quite excited by the youth," he added. "With England we've been crying out for some youthful exuberance and attacking play, and the lads have brought that. Not just in the game against Italy, but in training.
"It's great to watch and great to see. I think they're all very ready now to make their impression."
Sterling, in particular, earned rave reviews on just his fifth appearance for the senior team and the 19-year-old admitted he was keen to showcase his talents to the world.
"I was a bit nervous at the time but I just thought to myself it was a great opportunity to show the footballing world what I can do, and hopefully I showed some glimpses and helped my team to try and do the best that we could," Sterling said. "It was unlucky we didn't get the win but I thought we played some good stuff at times. On Thursday we'll be going at it again."