Ben Russell kicked a penalty in the first half for a Coventry side which suffered a yellow card and could not cope with the Rotherham pack.
Kleeberger scored two tries, one a penalty for Rotherham whh also had Henderson go over. West kicked two penalties with one for Whitehead.
Coventry's opening home play-off match is against Birmingham & Solihull on Saturday, March 27th (3pm).
On April 3rd, they entertain Moseley and the away match with Bees is on April 18th; the final play-off fixture taking place at home against Rotherham on May 1st.
You can buy your ticket to all 3 matches for just £30 (£25 for concessions) and children of 16 and under can attend free when accompanied by an adult. However, the offer ends on Wednesday.