The English Premier League champions on Saturday secured their first away win of the season in the 3-2 defeat of West Ham United at the Olympic Stadium.
"To be 2-0 down after seven minutes of any football match, be it in the Premier League or in your local Sunday League, makes it very hard to get a positive result".
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.
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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.
And with West Ham having picked up only two points in their last four league games, the pressure is on the home side.
"We spoke about the importance of starting brightly and playing on the front foot if we could, very similar to the other night, but we had to show real resilience in the second half".More news: US To Ban Electronics On Certain Flights
The east London club are not in any relegation danger, but the Croat knows a significant section of the home support are not happy.
Ayew and Michail Antonio fired wide and Andy Carroll had a goal ruled out, correctly, for offside as West Ham sensed they could haul themselves back into the game.
A goal from Andre Ayew made the final 27 minutes of the half very interesting, but the home side will have been left disappointed that they didn't get at least a point after creating some excellent opportunities.
"We have to find out why we are conceding so many goals and fix it because it is obviously harder to win games when you concede two or three goals in a game than if you keep a clean sheet".
"The second half was our best performance this season, but the ball just didn't want to go in".
"We have to believe and we always have to think positive", the 23-year-old stressed.
"In parts of the second half we were very good".
"You see centre-forwards go through that phase where they score and keepers, he has pulled off some crucial saves for us in the past couple of weeks".