The 30-year-old took 10 wickets in the opening match, including the decisive one of Brad Haddin, as the Three Lions earned a 14-run victory over Australia at Trent Bridge to take a 1-0 lead in the series.
"That was a wonderful game of cricket. The lower-scoring games are sometimes better because of the pressure and the situation and that is when you find out who your best players are, coming through it and playing well," Boycott told BBC Sport.
"I thought Australia were going to get home. Brad Haddin was getting away with it before lunch but England sussed him out and slowed him down, a bit of gamesmanship. Without Anderson they would not have got home."
The second Test gets underway on Thursday.