Dundee twice came from behind to level the game at 3-3 before a late Anthony Stokes header saw Celtic advance to the final.
"I couldn't have asked for more," McNamara told Sky Sports News. "I'm proud of the lads today, they gave us everything.
"I thought the players were exception, every single one of them. They gave everything they had and caused Celtic problems."
United are currently sixth in the Scottish Premier League.