"Leaving it too late is not something we do intentionally, our top six need to perform. As the tournament progresses, we need to get going, the batsmen are coming under pressure early and they need to bat freely," Dhoni said at the post-match presentation at the Sawai Mansingh Stadium.
The CSK skipper was full of praise for young Srikkanth Anirudha who played a six-ball 18-run unbeaten cameo towards the end to see the defending champions home.
"Srikkanth is an exciting youngster, you got to grab your opportunities, and that is what he has done. We have tried to bat him up the order but at times we need to continue allocating the same roles that we have done earlier," Dhoni said.
His counterpart Rahul Dravid said that Rajasthan are still alive in the tournament despite today's defeat, but accepted that they need to play some extraordinary cricket to qualify for the play-offs.
"You play a good game and sometimes a batsman comes out and plays an excellent innings, you got to accept that. The track was doing a bit, stopping and seaming around, they bowled well, credit to them.
"We are alive, just by our fingernails, we need to get going and try and win all the remaining games," he said.
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Ben Hilfenhaus, who was adjudged Man-of-the-Match for his impressive two for eight run opening spell, said the pitch helped seamers in the initial period of the match.
"It was very exciting game of cricket, good to come out on the winning side. T20 cricket is a funny format, things change rapidly. It was a good surface to bowl on, seaming around for me," he said.