Giacomo Bonaventura gave Atalanta an early lead at the Atleti Azzurri d'Italia before Fredy Guarin equalised in the second period. German Denis restored Atalanta's lead instantly before adding a third from the penalty spot in the 67th minute.
Rodrigo Palacio brought Inter back into the game in the 84th minute and Atalanta were reduced to 10 men when Facundo Parra was dismissed in stoppage time, but the Bergamese side held on.
The result leaves Inter four points adrift of Serie A leaders Juventus, but Zanetti insists one bad result will not give way to any soul-searching at the San Siro.
"It was a game with lots of chances for both sides. You have to accept the result, Atalanta played well," Zanetti told Inter Channel.
"Admittedly they had us under the cosh at times, but we responded superbly. They scored their second and third goals when we were on top, but that's part of the game and it won't alter the path we're on.
"Once it was 3-1 they were more in control of things, then at 3-2 we went looking for the equaliser but it never came.
"We did well fitness-wise, it was a hard-fought game, played at a high intensity and with plenty of chances.
"We knew it would be difficult at this stadium and against this team. I accept the defeat even though it could have finished differently and either side could have won."
Inter coach Andrea Stramaccioni was equally sanguine in defeat and felt his players were unlucky not to emerge with anything to show for their efforts.
"We were a little careless at the back at times but Inter always looked dangerous and we played at a high tempo," he said.
"This defeat won't douse our enthusiasm, we'll push on with our heads held high."