Transfer embargo-hit Pompey could find out on Thursday whether they can come out of administration.
Pompey, bottom of the table, face Spurs in the FA Cup semi-final on 11 April.
There was further bad news for Pompey as they also lost Armand Traore through injury.
However, Pompey were handed a reprieve as Fajardo's effort clipped the bar on its way over.
Pompey manager Harry Redknapp missed the post-match press conference as he is struggling with a virus.
The Football Association, meanwhile, has expressed its sympathy to Pompey fans over their club's plight.
O'Hara signed a new Spurs deal but will go on loan to Pompey until January.
The 28-year-old, 6ft 7in England international scored 16 goals in all competitions for Pompey last season.
But it was a very rare effort from Pompey and they soon went behind.
Predictably, the visitors' defence folded under pressure, with Pompey contributing two of United's goals.
But Pompey chief executive Peter Storrie insisted Adams was the best man for the job.
Pompey went behind to a stunning free-kick with Luis Aguiar beating David James from 30 yards out.
Birmingham immediately produced a spell of pressure to no avail, while Pompey grew in confidence and authority.
Pompey were docked nine points for entering administration in February and Avram Grant's side failed to recover.
It was a hammer blow to a Pompey side who had competed well in the opening period.
Al Fahim has been named Pompey chairman after passing the Premier League's fit and proper person test.
Birmingham started positively and Pompey goalkeeper David James needed to be at his sharpest in the early stages.
Paul Hart has been placed in charge of first-team affairs at Pompey, who host Manchester City on Saturday.
Pompey and England goalkeeper David James told BBC Radio 5 live of the "frustration" felt by the players.
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Pompey rarely looked like a side in sixth position in the Premier League but were gifted the lead.
Kranjcar provided Pompey with the perfect start after only four minutes with his first goal for the club.
Pompey continued to battle on and John Utaka hit the crossbar but the visitors, ultimately, proved too strong.
But doubts have continued to circulate about the property tycoon's financial backing, as Pompey toil on the pitch.
That proved the last of Pompey's forward play - in fact they then firmly hit the self-destruct button.
The Franco-Russian initially bought into Pompey as joint owner when he struck a deal with then-chairman Milan Mandaric.
But Pompey have improved since Alain Perrin took over and the visitors soon created chances of their own.
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Pompey midfielder Sean Davis was unlucky to be sent off with 10 minutes remaining after a second yellow card.
Pompey had been linked with the left-back but he signed a new four-year deal at Stamford Bridge on Wednesday.
He left for Pompey's bitter south coast rivals Southampton in 2004 but returned to Fratton Park in December 2005.
Pompey have also tied down reserve goalkeeper Asmir Begovic until 2011 after the Bosnian-born 21-year-old agreed a new three-year-deal.
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