Ranieri was dismissed less than nine months after leading Leicester to their incredible Premier League title success, with the team in danger of suffering relegation.
Shakespeare took charge on a temporary basis and oversaw 3-1 Premier League wins at home to Liverpool and Hull City, earning the right to lead the club to the end of the season, and Srivaddhanaprabha defended the decision to replace the Italian.
"It hurt," he said. "We didn't want this. But we see the club as the first priority. It's here for 133 years, so we try our best to keep it going. I don't think this will drag the club down.
"Claudio understands. He's also sad, but he said that he also understands that football will always come down to the results. We decided to make the club better.
"If we had kept him on and got relegated, to think back that we should have done something different back then - that's no use. We decided - and got six points - I think that's worth it."
Srivaddhanaprabha explained Ranieri's questionable tactical decisions were among the reasons why he was dismissed by the club, which was 5000-1 to win the Premier League title.
"We want to ensure that we're 100 per cent staying up, but his new method of changing tactics to improve the team was not working," the vice-chairman said.
"Players don't understand how to play and need time to adjust. The results were not what this town and also the world were expecting.
"I spoke since last year that Leicester could be in relegation battle this season because this is football, it is always uncertain.
"We knew that some change will shock the players and lead them fight more. In my view, the manager has to rely on their results."