The Foxes have moved five points clear of the Premier League relegation zone after collecting maximum points against fellow strugglers Hull City courtesy of goals from Christian Fuchs, Riyad Mahrez and a Tom Huddlestone own goal.
The victory came after a morale-boosting victory over Liverpool at the King Power Stadium on Monday night, giving the side their first back-to-back successes in the league this season.
"We spoke to the players before the game, they showed resilience and character," Shakespeare told reporters afterwards. "It was against the run of play after going 1-0 down, but to bounce back showed the resilience in our side.
"Results give players confidence. Back-to-back wins will give confidence for the last 11 games of the season.
"In terms of our points, it has been a turnaround. Everyone looked at the game against Liverpool on Monday and to get the three points under pressure was important but to back that up with another win was vitally important.
"We know the last 11 games will have twist and turns, we need to take care of ourselves."
The Foxes now have a two-week break before their next game, a trip to West Ham United on March 18.