The Citizens have all to play for in the return leg of the Uefa Champions League quarter-final tie after Heung-Min Son struck with a left-footed shot in the 78th minute to give Spurs an advantage.
Within the first 15 minutes of the encounter, Sergio Aguero missed a chance to put the visitors ahead at the Tottenham Hotspur Stadium after seeing his effort from the penalty spot saved by Hugo Lloris.
After Son's opener, Manchester City struggled to net an equaliser and had to settle for a defeat, however, Mahrez who was in action for 89 minutes in the encounter is confident that they can bounce back and make it to the last-four stage with a win at home.
"Not the best night but we can do it at home. Come on Man City," Mahrez wrote on Instagram.
Mahrez who was drafted in for injured Bernardo Silva struggled to find his feet in the first half of the encounter but returned with an improved composure after the restart.
His performance made Guardiola singled him out for praise despite the lack of support in some moments during the game.
"In the second half, he [Mahrez] was really good. In the first half, he was isolated when he had the ball he did not have support in actions two-against-one and one-against-one," Guardiola was quoted as saying by Manchester Evening News.
"When David [Silva] and Sergio [Aguero] moved to the left side there was a problem but he was aggressive and he delivered good crosses.
"We are going to put more people in the box next game - or maybe not, We will see!
"In general, my feeling is the team was so solid. We concede few chances and the team was able to create a lot of chances.
"I know how good they play long balls, second balls when they attack. They are a team who play more with transitions and more with physicality because they are strong, and we played so good.
"Now it is time for rest and recovery and next Wednesday at the Etihad Stadium I invite all of you."