Leicester have since won four successive matches in all competitions to move clear of relegation and reach the Champions League quarter-finals.
"There are a lot of twists and turns to come and we're proof of that," Shakespeare told reporters on Friday. "Three games ago in the Premier League we were down there and people were writing us off.
"The sooner we can secure our safety the better - it's our main focus. We've got two home games and it could go a long way in making sure we're safe, but also it could go the other way if we don't get the results we want."
Leicester will be without captain Wes Morgan, who missed the 3-2 victory at West Ham United, for Saturday's home match against ninth-placed Stoke City, as the central defender is yet to recover from a back injury.
"We're trying to give Wes enough time himself to see how he feels and then push him when he's right," Shakespeare added.
However, midfielder Danny Drinkwater is fit to face Stoke despite declining an England call-up due to a hip injury.
The 27-year-old Drinkwater chose to rest during the international break for fear of aggravating the problem.
"He's fine," said Shakespeare. "He got a few rest days, which he needed. Danny's is more of a hip flexor problem, brought on via fatigue. We'd like to thank England for their cooperation there."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Ed Osmond)
