Samuel Eto'o hit a 78th minute winner for Inter, who had fallen at the first knockout stage for the last three seasons. The Serie A side went through 3-1 on aggregate.
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"We were the best team by far. To win here was almost a perfect performance not just by the team but by the individual players," Mourinho, who left the London club nearly three years ago, told Sky Sports.
"I celebrated a lot in the dressing room because it was a big victory for my team. I love Chelsea, I love this stadium and I love these people. But I'm a professional and who knows I could coach another English team and come here again."
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Inter had missed the three best chances of the match before Wesley Sneijder sent Eto'o free and the Cameroon striker scored with aplomb as Inter fly the flag for Serie A as the only Italian team into the last eight.
"I think we dominated the game and there was no danger for us... when we were attacking we created the chances and the goal finally came and we should have got two or three," said Sneijder.
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Chelsea, who had reached the semi-finals in five of the last six years and last lost a home Champions League game four years ago, were desperately short of invention and barely troubled goalkeeper Julio Cesar.
Inter opted against trying to sit back and defend their first-leg lead and produced an energetic display in a first half that featured more appealing, complaining and theatrical over-reacting - from both sides - than constructive football.
Mourinho's tactic to start with three strikers - Eto'o, Diego Milito and Goran Pandev - seemed to catch Chelsea out and it took the Londoners a long time to get a hold on the game.
However, solid Inter defending, with centre backs Lucio and Walter Samuel in dominant form, and a sharp block by Cesar to keep out a Nicolas Anelka flick ensured a goalless first half.
Inter began to pile on the pressure midway through the second half and a clever backheel by Sneijder sent Pandev through but was thwarted by a terrific covering tackle by Yuri Zhirkov.
Four minutes later Milito sprung the offside trap but shot wide with just stand-in keeper Ross Turnbull to beat while Thiago Motta headed over the bar from a free-kick.
Chelsea were showing nothing at the other end and it was no real surprise when the impressive Sneijder looped a ball over the home defence and Eto'o, who had not
