The Argentine was in spectacular form in the final third and celebrated the landmark from close range early on.
Speaking on Monday Night Football, Carragher has outlined his belief that Liverpool will only be able to win the Premier League if City lose focus in the second half of the season as the Citizens look to win their first European Cup.
Meanwhile, Saints are now seven Premier League games without a victory and lie 16th.
Sterling doubled his goal tally on 67 minutes, as the winger received the ball from Aguero before firing a low effort across Alex McCarthy.
"We thought for him it's better to play, not for 90 minutes, but to play after two weeks without training".
Therefore, Pedro and Willian are expected to retain their places in the attack having both started against Palace on Sunday afternoon as Victor Moses continues to be frozen out under Sarri with the Nigerian not even making the squad. However, Roy Hodgson side failed to take their chances and Chelsea took the lead on 33 minutes. Willian then saw a goal disallowed for offside in the closing stages of the first half.
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The Citizens have won eight of their opening 10 matches, drawing the other two, and are out in front by virtue of their superior goal difference compared to Liverpool's.
Chelsea midfielder Mateo Kovacic has warned his team-mates not to slip up like Liverpool when they face Bate Borisov in the Europa League on Thursday evening.
"It is normal. Sometimes it is better to rest than always play".
Morata has scored 21 times in 63 appearances for Chelsea since arriving from the Bernabeu.
At the end of a tragic week for the Foxes, the Danish shot-stopper's impressive display in goal helped them keep a clean sheet in an emotional 1-0 win away at Cardiff on Saturday.
César Azpilicueta insists Chelsea have what it takes to challenge for the Premier League under Maurizio Sarri. "Obviously if we don't drop points, we have the chance to do it".