The Canaries triumphed 4-2 on aggregate after a 1-0 win at Carrow Road a fortnight ago to clinch their first piece of silverware in 28 years.
And Smith, who is joint majority shareholder at the club with husband Michael Wynn-Jones, was full of praise for former Norwich midfielder Adams.
“He was always one of my favourite players,” she said. “He was the best penalty taker, the best pundit when he retired and now he’s the best manager – he is wonderful.”
Smith hailed the performance of the young Canaries, who became only the second Norwich side to win the competition, following in the footsteps of the 1983 side that beat Everton.
The 71-year-old added: “All I can say is wow!”
“They have thoroughly deserved it and they played so well over two legs,” she said.
“They were just outstanding. They were calm, cool and very, very talented. What a lovely team and I think their manager is a top dog!”
Almost 3,000 Norwich fans were at Stamford Bridge, and Smith thought the cup triumph was the perfect end-of-season finale after the club ensured their Premier League survival on Sunday.
They were just over the moon. I think they were on a high before they got there after staying up yesterday and this was the icing on the cake.”
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