Luc Castaignos gave the Nerazzurri an early lead in the Dublin Super Cup encounter with a well-taken goal and Giampaolo Pazzini added the Italian side's second moments after they had Thiago Motta sent off.
Neil Lennon's team, who actually began their Scottish Premier League campaign last weekend, were unable to find a way past goalkeeper Luca Castellazzi when they did manage to break down the Inter defence.
Inter claimed the lead in the seventh minute as Goran Pandev played a one-two before slotting a pass through to Dutch forward Castaignos, who gave Celtic goalkeeper Lukasz Zaluska no chance at his near post.
The Italians were forced to make an early change when Yuto Nagatomo suffered a shoulder injury, with Marco Faraoni coming on. Inter had Motta and Dejan Stankovic booked, with Pandev lucky not to be yellow-carded too after lashing out at Beram Kayal.
Georgios Samaras almost levelled it in the 23rd minute when he raced onto a ball over the top from Charlie Mulgrew but his cushioned volley was diverted wide by the fingertips of Castellazzi.
The Inter stopper then dealt comfortably with a low shot from Scott Brown and somehow kept the Hoops at bay to deny Samaras and Mulgrew in quick succession.
Zaluska prevented Inter doubling their lead as he produced a fingertip save to deny Pazzini following Pandev's tee-up. The Macedonian was proving to be Inter's key creative force and his delicious pass played in Castaignos, who clipped the ball past the onrushing Zaluska but also wide of the post.
The temperature rose even higher in a tetchy friendly when Motta was sent off for a challenge on Brown, although the 10 men extended their lead seconds later.
A ball over the top caught out the Celtic defence and Pazzini got to the ball before Zaluska to prod it home right at the end of the first half.
Brown was booked for a foul on Faraoni, who then launched into a wild challenge on Cha Du-ri, and though he failed to make contact the South Korean took exception to it and both players were shown yellow cards by the busy Damien Hancock.
Inter Milan substitute McDonald Mariga saw a shot blocked as Celtic's defence again looked vulnerable, although they were unlucky not to pull one back 15 minutes from time when the substitutes Gary Hooper and Anthony Stokes combined.
Hooper played Stokes through on goal but Castellazzi was equal to his low effort. Inter substitute Faraoni then tested Zaluska with a rising drive as Celtic failed to get on the scoresheet.