The Algerian winger netted the opening goal in what was a dominant – and record-breaking – display from Pep Guardiola’s side in the Portuguese capital.
Bernardo Silva bagged a brace of goals with Phil Foden and Raheem Sterling also on the mark in what was City’s biggest-ever away win in the Champions League.
The margin of victory at the Estadio Jose Alvalade puts City in a dominant position going into next month’s second leg at the Etihad.
With the reigning champions nine points clear at the top of the Premier League and through to the fifth round of the FA Cup, it’s shaping up to be a hugely exciting and defining final third of the season.
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And with so much to play for, Mahrez insisted that there would be no easing up or drop in standards from the City squad - despite the pressure and expectations placed on them.
“We have the pressure in every match, but we don't think much about that,” Mahrez asserted.
“Winning this competition [the Champions League] is very far from now, we go match by match.
“The Champions League is never easy and the quality is higher, especially in the knockout games. We came here very focused.
“There is still another game to play and this season in the Champions League there are no away goals, it is not like before.
“But the next game at home, we are going to have the same focus and the same type of game. We are going to try to win again. The Champions League is not easy and not like a league.
"You have to be there in so many things and we have to be strong and arrive at the end.
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“On Tuesday we won, we played a great match we scored five goals, and this is the way to carry on in the next games.
“Now it's time to focus on the Premier League and try to play a good game against Tottenham.”
Mahrez’s goal on Tuesday extended his own impressive scoring sequence this season with the 30-year-old City’s leading scorer having accrued 17 goals across all competitions.
He also has now scored in eight of the last nine games for City to once again emphasise his superb quality.
But rather than focus about individual plaudits, Mahrez says he is simply happy to be able to try and contribute to the team’s quest for success.
“I am just here to try to help the team,” Mahrez asserted.
“Obviously, it is good when I score and it helps the team.
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“I am happy with how we won on Tuesday and it was good.
“I was there in the box when the ball arrived. It was strange because it took time to be given but at the end of the day you have to be there and I was there.
“We push each other and we are all in the squad to win games and that is important.”