Juan Mata's 13th-minute strike had given the visitors the lead but the hosts hit back to claim a famous victory thanks to second-half goals from Carlton Cole and substitutes Mohamed Diame and Modibo Maiga.
Allardyce said: "We started okay but when they scored we lost our confidence and momentum and the save just before half-time by Jussi (Jaaskelainen) was critical.
"So I needed to make some changes. We tried to freshen the team up, bring in some fresh legs. It was all about playing in the opposition's half and playing off Carlton Cole quickly.
"I think he was itching for a real good game, the way he was handling the ball. I thought our players were trying to play through midfield too much and getting it taken off them in the first half.
"So we went and played in the opposition's half and took the game to Chelsea. After 15 to 20 minutes we hadn't scored and I thought it might be a bit difficult. Then we scored but Chelsea came storming back and Jussi's had to pull off some great saves again and then we finished it off
"It shows the fitness of the team. In less than six days they have played three games against three of the big boys and we have come through with our fitness stats being absolutely brilliant.
"That has given us the opportunity to wins today's game along with the quality the players showed in the end."