Shakespeare's team moved to 10th place after a 2-0 victory against Sunderland on Tuesday.
Shakespeare's team moved to 10th place after a 2-0 victory against Sunderland on Tuesday that left beleaguered Black Cats boss David Moyes looking doomed to relegation.
The triumph extended Shakespeare's winning run at the start of his Premier League management career to five games and took the Foxes to nine points above the bottom three.
But Shakespeare, who replaced the sacked Claudio Ranieri, refused to accept the job of staving off relegation is complete.
"No, I am still not going to say that because I think we are never quite sure if other teams are capable of going on good runs," he said.
"I have been in football for long enough to know anything can happen.
"We have to make sure we stay focused and move onto the next one.
"We have to make sure we prepare for Sunday at Everton because that'll be another big test for us.
"We have to make sure we're ready for each football match.
"That's my job. We have to be competitive in every game but the idea is to try to win it and that's what we'll do until the end of the season."
Shakespeare admitted that his start to life at the helm had exceeded his own expectations, with his Midas touch extending to inspirational substitutions against Sunderland.
He made a double change, bringing on Marc Albrighton and Islam Slimani, and seven minutes later the pair combined for the opening goal before Albrighton teed up Jamie Vardy for the second.
"It doesn't feel easy, especially on the sideline," said Shakespeare.
"I've never felt really comfortable until the final whistle, so no, it doesn't feel easy.
"When I saw the games in front of me, starting against Liverpool, I couldn't have imagined this.
"I am really pleased with the impact of the substitutions because that is what you make them for."
Meanwhile, Moyes is enduring a far more torrid time than Shakespeare, with poor results on the pitch combined with controversy off it.
Hours before kick-off at Leicester, his club were forced to back him publicly over his threats to 'slap' a female reporter who recently quizzed him about his job security.
"I've been surprised in many ways (by the reaction) but I've done my job with the players, prepared them and organised them," he said.
"The world of football is a great business now, it employs an incredible amount of people, whether it be in the media or at the training grounds, and for that reason football is a big talking point.
"It was not difficult at all, I said and did all the things, prepared the players and did the same things we would do for any other game."
But Moyes conceded his rock bottom side, now eight points from safety, face an almost impossible task to save themselves from relegation after back-to-back losses at Watford and Leicester.
"It's tougher. I really felt that to give us a real chance we would have to win one of these two away games and they both were difficult on paper," he said.
"What I didn't put down was a win against a Manchester United or an Arsenal or Chelsea in our remaining fixtures so in my head I know have to win at least one of those games."