It is the first time in 15 seasons that the Nerazzurri will not be gracing continental competition and will further increase the pressure on young coach Andrea Stramaccioni, who watched his side fall to a fifth defeat in six Serie A matches.
Inter barely helped themselves, gifting Lazio a 21st-minute lead with an own goal and then, after equalising through Ricardo Alvarez, missing a gilt-edged chance to take the lead when Alvarez incredibly fired over an open net just prior to half-time.
It was to get worse before the break though, with Inter conceding a penalty which was slotted home by Hernanes.
Inter then missed a second-half penalty of their own, Alvarez's night steadily going downhill, before Lazio substitute Ogenyi Onazi wrapped up the points for the visitors with a fine third goal.
The result leaves Lazio in sixth position on 58 points, while Inter remain eighth on 53.
No doubt keen to turn around their poor recent form, Inter looked the more dangerous early on with Alvarez and Tommaso Rocchi both drawing good saves from Federico Marchetti.
However, it was Lazio who took the lead following an embarrassing mix-up in the Inter defence.
Antonio Candreva's right-wing cross in towards his team-mate Sergio Floccari near the penalty spot should have been dealt with by one of Inter goalkeeper Samir Handanovic or his two defenders Juan and Andrea Ranocchia, but the ball deflected between them before rolling into the net.
Inter levelled in the 33rd minute when Alvarez headed home Álvaro Pereira's cross - and they should have led three minutes from time but first Marchetti turned Esteban Cambiasso's brilliant shot onto the post, before Alvarez missed that incredible chance in the 42nd minute.
The hosts' misery was then compounded just before the break when Ranocchia fouled Floccari inside the area and Hernanes fired his penalty into the roof of the net to make it 2-1.
Inter came out after the break in determined fashion and Fredy Guarin (twice) and Mateo Kovacic both came close to equalisers.
The home side were then handed the perfect opportunity to get on level terms in the 70th minute when Lorik Cana brought down Guarin in the box to concede a penalty.
Alvarez could not take advantage though, slipping as he was about to take his kick and blazing his shot high over the bar.
Five minutes after that Lazio got their third goal, Onazi finding the top right-hand corner with a superb 30-yard free-kick as Inter's hopes of a top-five finish were shattered.