Brazil coach Carlos Alberto Parreira paid tribute to Croatia after the World Cup holders laboured to a 1-0 win.
"The challenge is not only the first game," Parreira said after Kaka's first-half goal set up the victory.
"In addition to the fact that the team hasn't played a lot together, we faced an adversary that was good and marking very well, with energy.
"I think the game was balanced, we had more shots on goal but we had a certain difficulty imposing our own rhythm."
Parreira insisted Brazil would improve in their second Group F game against Australia on Sunday in Munich.
"To win like we did is not ideal and we still have to convince"
Brazil captain Cafu, who helped set up Kaka's goal, added: "Without any doubt, the important thing is start on the right foot.
"I told the team before the game we had to go up seven steps, we went up one and now we have six to go," he said, referring to the number of matches Brazil will have to play to win a sixth World Cup.
Match-winner Kaka agreed with his captain that victory was the only important factor from Tuesday night but he admitted his side needed to "improve our movement, to be more creative and to mark better".
"We felt a heavy responsibility as it was the first game, and it was against the strongest opponents in our group - we respect Australia and Japan but we are traditionally stronger than them," he said.
"To win like we did is not ideal and we still have to convince and I'm sure the next game will be better as we will not feel under so much pressure."