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The world number two inspired Great Britain to win the Davis Cup for the first time in 79 years with victory over Belgium in Ghent over the weekend.
Captain Leon Smith urged the LTA to use that triumph to inspire future players, but Murray, 28, said he "did not know where the next generation are".
"Nothing ever gets done and I don't like wasting my time," he said.
The Scot added he has not discussed the lack of young British players competing in Grand Slams with LTA chief executive Michael Downey.
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"I don't speak to any of the people who are in a high-up position about that," Murray revealed. "I haven't really spoken to them about anything.
"It's concerning not to have any juniors in the Grand Slams because that is something we were always very good at. It's not ideal."
Downey earlier said Britain's Davis Cup win was a "special, emotional moment" that could drive interest in the sport.
Before the final in Ghent, Murray was criticised by former Great Britain Davis Cup captain David Lloyd for not putting enough back into the game.
"I'd rather concentrate on my own stuff and when I've finished playing, I'll have a lot more time to try and help or give back to the game," Murray added.
"Just now, I've just got to concentrate on trying to win as much as possible."
Murray said one of his main frustrations was a lack of players to practise with whenever he is in the UK.
After returning from the Shanghai Masters in October, Murray said he arrived at the National Training Centre in London to find no other players present.
"I was there on a Monday at about 3pm and then on Tuesday, at the same time," he said.
"There was not one person using any of the indoor courts and not one person in the gym. I took photos of it because the place cost like £40m and there are no people."
Prior to Murray's comments, Smith said the LTA needed to quickly create a long-term strategy to capitalise on his team's victory.
Smith also praised Judy Murray's tennis programmes but said the mother of British number one Andy and doubles specialist Jamie "needs a lot of help".
"She can't keep doing it on her own," he added.
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Murray leads the LTA's Miss-Hits programme - an introductory course for girls aged between five and eight - and a Scottish-based scheme, Tennis on the Road.
Smith, who became Davis Cup captain five years ago with the team a play-off away from relegation to the event's lowest tier, added: "At the end of the day, we all care about British tennis a lot.
"What we want to see is more people playing, so there should be a bigger talent pool in years to come.
"It really is an important time to get strategies rolled out as quickly as possible, not only to get people on the court but to keep them on the court.  We need to offer them good clubs and good coaches that turn up in all weather and bang out great sessions. Let's hope it has a positive influence, because it should do."
The LTA was criticised for failing to capitalise on Murray's Wimbledon victory in 2013 with participation levels falling in the aftermath.
But LTA chief Downey said the coverage created by Britain's successful weekend in Belgium should help "encourage participation".
In the most recent figures released by Sport England, for the six months up to March 2015, tennis participation was up.
Andy Murray says talking to the Lawn Tennis Association about the future of British tennis is a waste of his time.