The club have not released the full annual report, only selected highlights with no detailed explanation as to how £28.5million of extra costs have been incurred.
Mark Jensen, editor of online fanzine themag.co.uk, said he had expected profits for the 2013/14 campaign to be closer to £50million given the increase in income from television rights and the sale of Yohan Cabaye to Paris St Germain for around £20million.
Newcastle also reported revenues increased by 35 per cent from £95.9million to £129.7million. More than half of Newcastle's income - £78.3million - came from the Premier League television rights deals, with commercial income also increasing.
Jensen said: "This has just provoked more questions than answers. There is £28.5million of costs for which there is no explanation. The wages-to-turnover ratio is also not included.
"We had anticipated a profit of around £50m, especially with Cabaye being sold.
"The way that most fans look at it is that Newcastle didn't buy a single player in the whole season and sold Cabaye. Everyone knows how much these clubs are getting from TV so Newcastle fans would like to think more profit would mean more team strengthening but that has not been the case.
"There seems to be both a lack of transparency and ambition."
Newcastle finished 10th last season and are currently 12th in the Premier League table.
A Newcastle statement said: "Most significantly, the club reported strong commercial revenue growth delivering £25.6million in 2014, up from £17.1million in 2013. This 49.7 per cent increase was largely the result of two lucrative new deals with the club's principal sponsors, Wonga and Puma."
It is the fourth successive year the club has made a profit and cements Newcastle's positions in financial terms as one of the most successful in the top flight. Everton made a profit last season of £28.2m, Manchester United £23.9million, Chelsea £18.4m and Arsenal £4.7million while Sunderland lost £16.9million and Manchester City made a £23million loss.
Newcastle's debt remained static at £129million in the form of an interest-free loan from owner Mike Ashley - none of the debt has been repaid.
Newcastle managing director Lee Charnley said: "I am pleased to report a positive set of results which confirms the healthy financial position the club now finds itself in and is a reflection of the prudent and measured manner in which we operate.
"The club benefits from a supportive owner and is financially stable. This gives us a strong platform from which to grow, both on and off the pitch, a result of which means, as we move forward, we are able to net spend on the playing squad and invest in other areas of the business.
"The most pleasing aspect in this set of accounts has been the growth in our commercial revenue and it has been our strongest year yet in that respect.
"With our commitment to keeping ticket prices affordable for our supporters growing our commercial income has been crucial. The deals we struck with our two main sponsors, Wonga and Puma, together with a stronger focus on our commercial operations, have helped us achieve this growth.
"We believe financial stability will deliver positive on-field results for the club."
The announcement prompted an outbreak of sarcastic humour from fans on social media, with @GallowgateShots posting: "#NUFC fans flock to the streets in masses to celebrate their record profit win."