They did survive a penalty incident when Julio Cruz hit the post in 36 minutes but the spotkick award was a bad one.
And they did not deserve to lose the goal the way they did, David Pizzaro’s freekick wickedly deflecting off the Rangers wall and flying into the left corner of the net.
Rangers almost made the most sensational start when Barry Ferguson was given a shooting chance after just 21 seconds.
Thomas Buffel created the opening with great work on the left before playing in Dado Prso who laid the ball off to Ferguson but he shot high and wide.
In saying that, Inter had the ball in the net after two minutes although Obafemi Martins was clearly offside as he connected with Luis Figo’s freekick and Greek referee Kyros Vassaras immediately blew his whistle.
Santiago Solari then tested Ronald Waterreus with a left foot shot from a tight angle but the Dutchman dealt with it comfortably.
However, Rangers were excellent in the first half. Their passing was crisp and they created decent opportunities although they did survive a highly dubious penalty award and some considerable Inter pressure.
The best Rangers chance fell to Peter Lovenkrands, back in the side set up in a 4-4-2 formation.
It was a great move in nine minutes as Ferguson worked the ball wide right for Hamed Namouchi who then found Buffel ahead of him.
Buffel swung the ball to the near post and Lovenkrands got in ahead of Walter Samuel but drove his right foot volley past the post.
Then in 17 minutes Namouchi found himself clean through on the Inter goal after a mistake by Marco Materazzi but he was unable to get the ball under control to get a shot in and Ivan Cordoba tidied up.
The Tunisian midfielder tried his luck from distance in 26 minutes but it was no problem for Inter keeper Julio Cesar
And in 28 minutes Buffel also eked out a chance when Lovenkrands laid the ball off to him on the left edge of the box but the angle was too tight and the Belgian fired his shot wide.
Inter, perhaps frustrated, picked up yellow cards in 29 minutes and 34 minutes when Figo fouled Olivier Bernard and then Cordoba hacked down Prso.
However, they were given a golden opportunity in 36 minutes when the referee was conned into giving them a penalty.
It was a mistake by Bernard which led to the incident. He gave the ball away to Figo 40 yards out and the Portuguese star quickly played in Martins who then sent Julio Cruz charging through on the left side of the box.
Waterreus raced off his line and clearly pushed the ball away before Cruz went tumbling to the turf.
Vassaras bought it and awarded a penalty and also booked Waterreus.
Justice was done, however, as Cruz thumped the spotkick against the right hand post and Rangers survived.
There was more trouble for Rangers before half-time, however. Ian Murray gave the ball away to Figo in 39 minutes just inside his own half and he sent Martins bursting away on the left side of the box.
Julien Rodriguez did well to match the Nigerian striker’s run and forced him to shoot wide.
Two minutes later Figo missed a fantastic opportunity when Solari crossed from the left and he headed down into the ground and over the bar from eight yards.
The Light Blues made it to the break intact but they were undone four minutes into the second half in the most frustrating and unfortunate circumstances.
Murray and Ricksen sandwiched Martins as he burst towards the box and it was a simple decision for the referee to give the free kick.
David Pizarro drove the dead ball low and it deflected off the Rangers wall sending it spinning into the top left corner of the net.
It was a cruel blow for the Ibrox men who had coped so well with the mighty Italians when many were expecting a slaughter.
If they experienced good fortune with the penalty miss, it was rotten luck to lose the goal the way they did.
Encouragingly, they did not capitulate and managed to carve out another decent opportunity in 62 minutes.
Bernard won a corner on the left and took it himself, swinging the ball to the near post area where Namouchi made a great click but Prso did not read the move and Materazzi was able to clear.
More poor refereeing almost gifted Inter a second goal in 73 minutes. Rodriguez mader a perfectly good challenge on Cruz but the official blew for a foul and then allowed Inter to take it quickly.
Alvaro Recoba, who had replaced the injured Martins, played in Solari who seemed certain to score but completely mis-controlled the ball at the vital moment.
Alex McLeish went for it in the final moments sending on Franny Jeffers and then both Federico Nieto and Stevie Thompson giving him FOUR strikers but they just could not find an equaliser.
Rangers may have lost in the San Siro but they can be proud of their efforts.
INTER: 17-Julio Cesar; 2-Cordoba, 25-Samuel, 23-Materazzi, 33-Wome; 7-Figo (13-Ze Maria 75), 8-Pizzaro, 19-Cambiasso, 21-Solari (18-Kily Gonzalez 84); 30-Martins (20-Recoba 59), 9-Cruz.
Subs not used: 1-Toldo, 5-Stankovic, 10-Adriano, 16-Favalli.
Bookings: Figo (39), Cordoba (34)
RANGERS: 25-Wattereus; 2-Ricksen, 14-Kyrgiakos, 16-Rodriguez, 3-Bernard; 31-Namouchi (19-Thompson 89), 6-Ferguson, 24-Murray (23-Nieto. 83), 26-Lovenkrands; 4-Buffel (21-Jeffers 77), 9-Prso.
Subs not used: 1-Klos, 5-Andrews, 12-Malcolm, 18-Pierre-Fanfan.
Bookings: Waterreus (36)
Ref: Kyros Vassaras.
Man of the match: Soto Kyrgiakos