Kalou went down under a clumsy challenge from Walter Samuel just before half-time when the score was 1-0 to the home side.
No penalty: Kalou appeared to be fouled by Samuel
Spanish official Manuel Gonzalez waved away the Chelsea protests with Kalou going on to grab an equaliser before Esteban Cambiasso restored Inter's advantage ahead of the second leg.
Kalou was quick to refer to the incident post-match and while Mourinho accepted it ought to have been a spot-kick, he also claimed the Ivory Coast striker knew what he was doing when he hit the turf.
'We were a bit lucky,' he told Sky Sports, 'but Kalou was clever. He dived at the right moment. Normally it's a penalty.
'The referee looked over to the linesman and the linesman told him no.'
Mourinho was happy to have eked out a narrow lead before his eagerly-awaited return to Stamford Bridge.
He added: 'It's an advantage. It's different to go there with a draw or a defeat than to go there in front.
Harsh on Chelsea: Mourinho believes the Blues should have been awarded a penalty
'When the game starts at Stamford Bridge, in the first second of the game Inter will be in the quarter-finals and Chelsea will be out.
'After that we will see, there will be another 90 minutes but at the start. 'Mentally that is an advantage.'
Up for the battle: Inter midfielder Cambiasso
Mourinho was today hailed by Inter owner Massimo Moratti for getting the better of former AC Milan boss Carlo Ancelotti, now in charge of the west London club.
'I had no doubts about my team. Knowing my players and, above all, knowing Mourinho, who had prepared this match well,' he said on www.inter.it.
'Putting on (Mario) Balotelli at the end of the match is typical of a coach who thinks about the best victory rather than about himself. 'He knows how to change his team with different systems and change it according to the situation.'
Esteban Cambiasso, who scored the winning goal in Wednesday night'sgame, insists the tie is far from over and expects a ferocious contestin the return leg at Stamford Bridge.
'The second goal gave us more security for the rest of the match, now we expect a battle in the second leg.
'I remember the last game that we lost against Manchester United inEngland and I really don't want that to get repeated. We are all goingto do what is possible to be able to get to the next stage of thecompetition.'
It was a penalty! Kalou blasts referee for failing to award Chelsea spot-kick Bridge calls time on England as full-back fears 'divisive' Terry reunionSpecial KO - Petr Cech injured as Jose takes control of Champions League tieCHELSEA FC