Zebre led by two points with ten minutes remaining after Gonzalo Garcia's superb long-range penalty, but Dan Parks' drop goal and a final-minute penalty gave Connacht a 23-19 win.
In January they were on the wrong end of a 16-15 scoreline against defending champions Ospreys at the Liberty Stadium, and ahead of two home games against Scarlets and Edinburgh Gajan admits they prefer away days.
"We could have beaten Connacht twice, and away to the Ospreys," Gajan told Onrugby.it.
"Above all away from home we have played well and could have got more out of games than we have.
"Playing in grounds where there is a lot of history, with the stands full and so many fans helps the players.
"It doesn't matter that the fans aren't supporting you, the atmosphere can drive you on. At Parma it's been a little more difficult.
"It's true that we still haven't won a game but this year was also about the content, the basics for the future.
"The sporting assessment is negative in terms of results. I'm not stupid, I realise that."
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