Best, who saw a header hit the post, formed an eye-catching partnership with Robbie Keane as the Republic drew 1-1 with the Super Eagles at Craven Cottage.
Trapattoni said: "I look at the performance and the personalities of the new players like Sean St Ledger and Leon Best and I'm pleased.
"I was a little bit afraid before this match because Nigeria are not just one of the best sides in Africa, but in the world. They are faster and stronger than European teams and are also very at ease with the ball."
Trapattoni added: "Leon did well as he was up against a tough Nigeria defence and he was particularly strong in the air.
"He showed he can be a strong target man and this is what we want because it allows Robbie to have the space to play between the midfield and the striker. I'm pleased with him."