The 57-year-old Spaniard, known as 'Fabri', replaced Juan Roman Rocha last week, but failed to galvanise the struggling Athens club as his team produced an uninspiring display against a well-organised Giannena outfit.
"Generally the team did not function well in any department, however, this team is Panathinaikos and I expect things to improve," Fabri told reporters.
"We threw away the first 20 to 25 minutes and only stayed on level terms due to some good fortune. A club like this one should not be struggling so much... There were some serious errors tactics-wise and it is going to take a lot of work to find the right formula and get the team competitive again."
The result meant Panathinaikos stayed in ninth spot in the table with 21 points from 17 matches.
The Greens, however, trail the league leaders and reigning champions Olympiakos Piraeus by a massive 24 points, as Leonardo Jardim's team maintained their imperious form with a 1-0 win at Levadiakos on Saturday.
Super League top scorer Rafik Djebbour headed home the only goal of the game in the seventh minute of added time - his 14th strike of the season - to clinch all three points for the Red and Whites, who remain unbeaten this season.
"When you win such a match in the last minute against good sides like Levadiakos then you are definitely heading in the right direction to win the title," goalkeeper Balazs Megyeri said.
"It's hard to predict whether we can win the championship undefeated. It's a given that we go out to try to win every game and if we manage to go unbeaten then it would be a great achievement."
There was much-needed joy for strugglers AEK Athens after the cash-strapped club earned a vital 1-0 home win over Xanthi on Saturday. It was only their fourth win of the campaign.
Antonis Petropoulos, who recently joined from city rivals Panathinaikos, scored the game's only goal after 68 minutes for Ewald Lienen's team, who stay in the relegation zone in 15th in the 16-team table.
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