Zebre remain winless after three rounds with Saturday's result coming on the back of defeats to Newport-Gwent Dragons and Connacht.
But the five-tries-to-one loss against the Gunners was the heaviest so far and Gajan insisted the club's detractors can say what they want but nothing will make him waver from his job in improving the club's players and the game in Italy at large.
Zebre scored one try at Murrayfield through full-back Sinoti Sinoti and Gajan believes they could easily have had another, as well as limiting their hosts to four tries.
"It's a difficult moment because we are working a lot and with honesty and we are not seeing the fruits of our efforts, neither in terms of the final score nor by remaining in the match until the death," said Gajan.
"The game could have finished four tries to two in favour of Edinburgh - whoever saw the match will be able to understand that.
"The points gap doesn't coincide with the difference between the two teams on the field and Edinburgh are certainly the strongest opponents we have met this season.
"But this is not an excuse; whoever wants to criticise can freely do so.
"To me and to my staff what interests us is that we continue to grow the Italian rugby movement as much as possible, and to develop Zebre players."
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