Chelsea supporters were asked to rate the performance of the key men Abramovich has tasked with running the club over the last 12 months.
In total, only 32 per cent of supporters think Abramovich's regime, in the form of chairman Bruce Buck, chief executive Peter Kenyon and the club's directors, have done a "good" or "very good" job.
Again, this is a significant fall with the comparative figures standing at 75 per cent in 2006 and 47 per cent last year.
The poll was conducted by independent research company Football Fans Census as part of the Evening Standard's annual London Football Report.
The figures also show the lack of faith supporters had in Avram Grant, prior to his sacking at the weekend, compared to his predecessor Jose Mourinho.
In the 2007 London Football Report, the Portuguese was voted the capital's most popular boss with 97 per cent of those surveyed saying he had done a "good" or "very good" job.
The comparative figure for Grant in 2008 was 63 per cent despite Chelsea's late-season charge.