I know people don't like it much if you say anything criticising Warne on this forum, but I will still dare to give my explanation.
It's full credit to Indian batsmen of course. They have much more decisive footwork against spinners.
This is when Warne in my opinion has struggled to trouble them given he lacked as much variety. Of course he didn't miss that variety against batsmen from other parts of the world who have far more uncertain footwork. They didn't know when to go forward and when to stay back against quality spin and could be foxed with big turners falling at a good length. Qualitatively, I think that's the slight difference between the two bowlers.
It's not that I underrate Warne. I put him in top 5 bowlers of all time. I fully appreciate the importance of his contribution. I just speak too often on Murali/Warne issue because I feel Murali gets hard done, partly because of his own humble conduct and partly because Warne had been put at a very high pedestal (deservingly so) a few years before Murali's emergence and no one it seemed was willing to undo that so quickly.
And I am massive Murali fanboy, I admit. I almost loved it when Murali took wickets against India, despite being an Indian supporter in general
EDIT: And yes, I was always relaxed when Warne bowled against India. Every single time.