Danilo D’Ambrosio and Ashley Young scored in the opening 20 minutes as Inter finished the season with 82 points, one behind champions Juventus.
Inter Milan clinched second place in Serie A, disparagingly described by coach Antonio Conte last month as the "best of the losers" when they ended Atalanta's 19-match unbeaten run with a 2-0 away win on Saturday.
Danilo D'Ambrosio and Ashley Young scored in the opening 20 minutes as Inter finished the season with 82 points, one behind champions Juventus who lost their final game 3-1 at home to AS Roma.
Atalanta, whose last defeat was at home to SPAL in Serie A in January, finished third with 78 points and were top scorers with 98 goals — two short of becoming the first side to score 100 in a season since 1950-51.
The hosts appeared to have one eye on their Champions League quarter-final against Paris St Germain on Aug. 12.
"For us, it has been a very hard and difficult year in all respects, including personal," said Conte after the game. "There has been a lot of criticism."
"We won 43 points away from home, we have the best defence, the second-best attack and the fewest defeats.
"The credit goes to these guys, to the people who have worked with them in the midst of the thousand difficulties that there have been in terms of injuries."
Inter Milan were off the mark in less than two minutes when Atalanta goalkeeper Pierluigi Gollini flapped at a corner and D'Ambrosio headed into the net. Gollini was injured in the process and had to be replaced by Marco Sportiello.
Ashley Young extended Inter's lead with a delightful goal after 20 minutes, cutting inside and then curling the ball past Sportiello from the edge of the area.
Last month, Conte, frustrated after seeing his team let several games slip from their grasp, said he was not interested in the race for second place.
"I say it's the first of the losers. There are those who are content with this, but it has no meaning for me," he said.