"We had to work hard and use the ball well. They're a great side, they came back to 1-1, but you can't beat it," he told Sky Sports 1.
On his own return, he added: "It's always nice to come back at home, whenever it comes you've got to take it and get on with it.
"I've been training hard, working hard, and it's great to be out there."
Carroll again captured the attention as he seized on farcical defending to open the scoring in the sixth minute and Campbell said: "They had to double up on him. Andy's going from strength to strength, winning headers and long may it continue."
Full-back Jose Enrique, who also played his part in a superb defensive effort, paid tribute to Campbell and Steven Taylor, who played in the absence of Mike Williamson and Fabricio Coloccini.
"The two centre-backs played their first game and they played really well," the Spaniard said.
"Chelsea are a really good team, we played really well in defence. I think we deserved a draw today and we are really happy with that.
"We had to drop back, it's normal against this team. If not, we lose maybe 6-1."