Giacomo Bonaventura put the home side ahead on nine minutes, before Fredy Guarin levelled just after half-time.
But, two goals from German Denis opened up a 3-1 lead and though Rodrigo Palacio pulled a goal back for Inter late on, it was too little too late.
“Inter did not deserve to lose, but we can only tip our hats to our opponents," he explained to reporters after the game.
"We were late defending Giacomo Bonaventura’s goal, but for the rest I was not disappointed with the team.
"Unfortunately, Atalanta scored their second during our best moment of the match. It is a shame, as if we had not conceded the third then we would have easily equalised again, as they were getting tired.”
La Dea striker Denis shared his delight after scoring two goals in the victory, but acknowledged the importance of not getting carried away with the result.
"We must have our feet on the ground," he told Sky Sports.
"Tonight against a great team we played well, this was our best performance of the season and we need to build on this because our main objection is to stay in this league."