The Italian took over from Martin O'Neill at the end of March, and he helped turn their fortunes around including their biggest derby win over Newcastle in more than 50 years.
"I have to be honest, yes I think we would have gone down," said the Italian.
"In my opinion this team was down. Some people said I would be too hard and would stress the players but we have recovered mental energy.
"Stephane Sessegnon, one goal in six games. Under me two goals in four games. Improvement.
"Under me, 1.3 points per game instead of one point per game. We would have finished top 10. Improvement.
"Eight points in six games without a striker. With Steven Fletcher, the top scorer injured. [Skipper Lee] Cattermole out for a long time. This is part of the job.
"Only the future can tell if I'm right but I think Paolo Di Canio will be right. I hope we can celebrate one day."
Di Canio also gave his backing to friend and compatriot Roberto Mancini after he was sacked at Manchester City.
"It's not easy when you've got big egos like Carlos Tevez. With Mancini he had a simple difficulty: he had seven top hot-headed footballers. One or two you can handle, but not seven," he said.
"Also players are piranhas. They smell if you are weak. Mancini started something political with the board. The players knew. They saw a fault-line. It was easy for them to say 'now we relax'. If they think you are weak it will change the dynamic."