However, Lane does not believe the added publicity contributed to the wicketkeeper's disappointing showing.
"I felt that was all dealt with and left back in England," said 45-year-old Lane. "We've spoken about the situation and Sarah felt very comfortable that it had been left behind.
"There's expectation on all of our players, we play a lot of games on television, we are getting judged and people will form opinions. With rewards come responsibility.
"Sarah is a key player, but we don't rely on one player. There's not been enough contributions from the batters."
Mark ButcherFormer England opener and Test Match Special pundit
"England would have prided themselves on their fielding but some of the catches that have gone down in the games they have lost have been crucial. The batting, with Sarah Taylor making three ducks on the trot, has not been as good as expected. Apart from Charlotte Edwards' century against India, nobody has come in and made a really big score."
Captain Charlotte Edwards, in her fifth World Cup, was the only England player to score a hundred, becoming the highest run-scorer in women's one-day international cricket in her 109 against India.
At 33, the Kent batter has admitted that the 2017 World Cup seems "a long time away", but Lane has backed the skipper to continue, with this summer's Ashes and the 2014 World Twenty20 on the horizon.
"She's as fit as she's ever been and is playing as well as she's ever been," said Lane. "She is a very inspirational leader, very honest with the group and very true to her herself.
"She has years of cricket nous and experience behind her. People keep talking to me about Charlotte retiring, but that's not on the radar.
"Lottie will know when the time is right but, before then, she's got my full support. I don't see her retiring imminently."
England meet New Zealand in the third-place play-off in Mumbai on Friday.
You can hear the full interview with Mark Lane during Test Match Special's coverage of England's third-place play-off against New Zealand on Friday, on 5 live sports extra, mobiles and online.
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