President Barack Obama rebutted Romney's assumption that the US's military strength had been reduced in the last four years saying: "You mentioned the Navy and that we have fewer ships than we did in 1916. Well, we also have fewer horses and bayonets, because the nature of our military's changed."
The hashtag #horsesandbayonets went straight in the Twitter trends list.
"Retweet if you think Obama won the debate. Invest in horses and bayonets if you think Romney won," tweeted Big Bird.
"We need more unicorns and laser guns, #horsesandbayonets," wrote user CourtneyPants.
Talking about the war in Syria and Iran, the Republican candidate said: "Syria is Iran's only ally in the Arab world. It's their route to the sea."
Critics were quick to point out that Syria and Iran do not share a border and that Iran already has maritime access through its Persian Gulf coast.
"Awkward #Romnesia Moment. Whoops, #Romney must be using Iphone5 Map App!" tweeted Rossssc.
The gaffes represented a blow to Romney's efforts to depict himself as a credible US commander in chief.
"For God's sake, will someone tell Romney how to download one of those world atlas thingies?" tweeted Steve Silberman.