"Although the Europa League was won, a reduction in income from that success compared with winning the Champions League in 2012 contributed to a loss for the financial year of £49.4 million," the club said in a statement on Tuesday.
FFP regulations state a club can have a deficit of no more than £37m a year, but head of communications Steve Atkins told Reuters that because of complicated accounting rules, Chelsea's actual loss was around £34m.
"Group turnover of £255.8m for the 12-month period is a record figure for the club despite elimination from the Champions League at the group stage last season," Chelsea said in their statement.
"A 19 percent rise in commercial income from £67m to £79.6m is a clear indication Chelsea is moving in the right direction in terms of business growth, as is a turnover figure that increased for a fourth consecutive year despite diminished European competition revenue."
The year ending June 2012 was the first time Chelsea had made a profit since Russian oligarch Abramovich bought the club in 2003.
"The latest financial result combined with the previous year's profit of £1.4m means for the first monitoring period for FFP regulations - which spans the 2011/12 and 2012/13 seasons - we will fall comfortably within the break-even criteria set by UEFA," the club said.
"We have the fifth highest revenue of all football clubs in the world according to the latest published Deloitte figures."
Chelsea are performing creditably on the pitch this season.
With Jose Mourinho back holding the reins as coach for the second time, the team occupy third place in the Premier League and are through to the last 16 of the Champions League where they will meet former striker Didier Drogba's Galatasaray.
Chelsea have put pen to paper on major new partnerships with Audi, Delta and Azimut Hotels.
A 10-year extension to a global agreement with Adidas was announced in June 2013, meaning the financial boost from the biggest deal the club has yet to sign will be recorded in the 2013/14 accounts.
"From the very beginning of the current ownership of Chelsea...a long-term objective was financial sustainability and the subsequent implementation of Financial Fair Play by UEFA and by the Premier League has brought that to the top of the agenda for football clubs," said chairman Bruce Buck.
"By our own analysis we are progressing from a commercial viewpoint as well as continuing to add trophies to our collection which we never lose sight of as our most important goal."
Chelsea have altered their recruitment policy in recent years, investing in younger players like Belgian internationals Eden Hazard and Kevin De Bruyne and Brazil playmaker Oscar.
"Our philosophy is we build upon success on the pitch," said chief executive Ron Gourlay.
"Although in these financial results we haven't repeated the sizeable profits made the previous year from player transfers, we believe the age profile of the existing squad means we will benefit from that investment for many years to come."