It was his team's fifth consecutive league win since he took over from Claudio Ranieri, who was sacked in February less than a year after leading the club to their first top flight title.
Shakespeare's players moved up to 10th place - nine points above the three relegation place.
"We're not safe 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's match 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."
City's opening goal came seven minutes after Shakespeare brought on Marc Albrighton and Islam Slimani. The former set up the latter. And after 78 minutes Albrighton was again the provider as Jamie Vardy struck the second.
"I am really pleased with the impact of the substitutions because that is what you make them for;" added Shakespeare.
While Shakespeare enjoyed a mid-spring night's dream, his Sunderland counterpart David Moyes is facing a relative tragedy.
His team are bottom of the Premier League - eight points from safety - following back-to-back losses at Watford and Leicester.
"I really felt that to give us a real chance of survival we would have to win one of these two away games," 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."