West Ham have upcoming trips to Hull City and Arsenal, before returning to the London Stadium for their next home game against Swansea City on April 8.
"We shouldn't be 2-0 or 3-1 down in the first minutes of the game".
Mahrez scored the first in the fifth minute, although his curling effort from the right was nearly certainly a cross intended for either Shinji Okazaki or Vardy, who had given him the ball.
Leicester were forced into a significant change to their preferred line-up, with captain Wes Morgan ruled out by a back injury sustained against Sevilla.
West Ham manager Slaven Bilic echoed Shakespeare's appraisal of Schmeichel, adamant his side would have got something from the match had the Dane not been quite so impressive.
Among the banners in the home section was one which read' Long Live The Boleyn' in homage to the club's old stadium as they struggle to settle into their controversial new one.
West Ham United host resurgent defending Premier League champions Leicester City this afternoon, kick off 3pm.
After only five minutes, Riyad Mahrez swung a hopeful cross into the West Ham penalty area; the ball evaded everyone and went straight into the goal.
Robert Huth made it 2-0 when left totally unmarked to head home Marc Albrighton's cross.
Manuel Lanzini briefly halved the deficit with a free-kick but West Ham were booed off at half-time, and although Andre Ayew pulled another back after the break Leicester resisted a late rally to claim all three points. But it did rock West Ham and the visitors capitalised ruthlessly.
Subs (not used): Nordtveit, Feghouli, Adrián, Collins.
A smart interchange between Mahrez and Albrighton won Leicester a corner.
Subs (not used): King, Amartey, Zieler, Gray.
The Hammers went into this clash against a rejuvenated Leicester City side knowing they were in need of three points, having not tasted victory in the previous four league games. We started really well and got the goals but it was backs to the wall at the end.
"We have to give West Ham credit", Leicester boss Shakespeare told BBC Sport.
Kasper Schmeichel was at his very best to make a vital late save, while an terrible Ayew miss let Leicester off the hook and saw the match slip away from West Ham.