Sturridge scored a hat-trick for his sixth goal in the past four Premier League matches as Liverpool came from behind to win 3-1 at Fulham.
Gerrard is now likely to miss England's friendlies against Ireland at Wembley on May 29 and away to Brazil on June 2.
The result sees Everton maintain their five point lead over their rivals and are looking primed to beat their rivals to a sixth place.
City's woeful run this season has forced them to crumble down in the UEFA rankings table.
The win lifted Liverpool's spirits but not their position in the standings, where they remain seventh.
Fans have applied to their local councils to register the two grounds as "Assets of Community Value".
Suarez's suspension begins immediately, meaning he will miss the last four games of this season and the first six of the next.
Rodgers launched a robust defense of the striker and said the punishment was given against the man rather than the incident.
Suarez was punished on Wednesday by the English Football Association after he bit the arm of Branislav Ivanovic at the weekend.
Liverpool and England captain Steven Gerrard is likely to need shoulder surgery at the end of the season, the Premier League club said on Wednesday.
The suspension rules the Uruguay international out for the final four league matches of this campaign and the first six of next season.