Chelsea meet Tottenham tomorrow at Wembley.
Chelsea won the tournament twice during Mourinho's first reign at Stamford Bridge, but haven't claimed it since he left in 2007.
Tottenham beat them in the final a year later, but Chelsea have not got that far again until now.
Mourinho doesn't think the club have anything to be ashamed of and added: "Chelsea cannot win everything every season. If you want to do that, you have to change countries to one where the competition is not so hard and to win titles is an obligation.
"Chelsea in the last 10 years won just the League Cup twice. Many times they were at Wembley, winning FA Cups, and won the Premier League and European competitions.
"Now, with a new team and people who were not in dozens of finals at Wembley, we will try to make Wembley something 'normal' for us, 'normal' in the sense that we will try and get there year after year.
"I have affinities with every competition. I respect every competition. It would be easy now because we lost against Bradford to say we didn't take the FA seriously, but we did.
"Probably lots of teams follow us since 2004, 2005, 2006, 2007 when we took the League Cup as a real competition, a real challenge, and we were trying to reach finals and to win.