The former Leicester and Chelsea full-back was charged with leading the team into their 1-0 defeat at Coventry after Paul Groves was sacked earlier in the week.
But when asked is he was interested in the job, Rofe said: "That's never entered my head.
"I was asked to take the team and that's what I've done and the powers that be, above me, will decide what happens in the future."
The Cherries immediate future lies in the League One relegation zone after David McGoldrick's 62nd-minute strike saw the Sky Blues leapfrog their struggling opponents.
Bournemouth had chances to open the scoring but did not take them - Lee Barnard wasting the clearest opportunity when through on goal two minutes before the opener.