Second-half goals from Shinji Okazaki and Islam Slimani at the King Power Stadium guided the Foxes into the fourth round at Liverpool’s expense.
Coutinho played from the start, following on from his first Premier League outing of the campaign against Burnley at the weekend, after an opening to the season that saw the Brazilian pursue a move to Barcelona and spend time sidelined by a back injury.
Jurgen Klopp revealed after the match that his plan was always to withdraw Coutinho, but Shakespeare says emerging for the second half and not seeing the playmaker involved gave his side a welcome boost.
“We led a charmed life in the first half,” he said.
“We know that our goal was under threat. I was just delighted to get in at half-time and then even more delighted to see they took Coutinho off.
“That was one of the main contributions to us for the second half.
“You worry about your own team’s performance and we asked them to be more aggressive in the second half. We needed better hold up play from the center-forwards in the second half.
“We wanted to play on the front foot a bit more. Shinji got his chance due to an injury to Leonardo Ulloa, but I thought that was a key moment for us as well.
“You could see the response in terms of Shinji getting in and around people and it was a major factor in contributing to the win.”