Divock Origi scored in the sixth minute of stoppage time to pinch three points for the hosts.
Wild scenes ensued inside Anfield and Robertson has praised his teammates for their strong character.
"What a finish – he [Origi] just reacted so quickly," Robertson told Liverpool's official website . "I'm not sure he knew what to do once the ball went in, but it was a perfectly good goal and we got the three points.
"I'm sure there'll be a few tired bodies, but it's well deserved and it's all worth it when you go home and you're sitting with your family with three points in the bag.
"Man City had the benefit of playing first this week and we knew they had won, so we didn't want them getting too far in front. We stay right on their tails – another massive win for us."