But 23 points from Ireland fly-half Jonathan Sexton, as well as two scores from Isaac Boss and Leo Auva'a, were enough for Leinster to claim the win and deny Edinburgh a losing bonus point.
However Visser, who moved to the top of the RaboDirect PRO12 scoring charts with five tries, is adamant Edinburgh can take confidence from their performance against Joe Schmidt's side.
He said: "We are gutted to lose but we were in it for long parts of the game.
"We have to take the positives out of the game, we can challenge the big teams and we can stay in the game for so long.
"I am happy to get some tries after a slow start to my season."
But Visser warned his colleagues that they will only be able to beat the best sides in the RaboDirect PRO12 if they improve their discipline after conceding 21 points in penalties.
"It was an outstanding game to watch except for the penalties we gave away.
"We were outstanding attacking but our penalty count let us down."
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