England went down 3-2 on penalties in a shootout after a 1-1 draw with Italy at Wembley Stadium.
Marcus Rashford, Jadon Sancho and Bukayo Saka missed spotkicks and have since allegedly copped racist abuse.
“I’m not totally across everything, but my first thoughts this morning are with the boys that have done so well for us,” Southgate said.
“The players have had such a great togetherness and spirit and brought our country together. They should be, and I think they are, incredibly proud of what they have done.
“For some of them to be abused is unforgivable. Some of it has come from abroad, we have been told this, but some of it is from this country.
“It’s not what we stand for. We have been a beacon of light to bring people together and the national team stands for everybody. That togetherness has to continue.”
England players have taken to social media to offer them support, led by captain Harry Kane.
Kane tweeted: “Three lads who were brilliant all summer had the courage to step up & take a pen when the stakes were high.
“They deserve support & backing not the vile racist abuse they’ve had since last night. If you abuse anyone on social media you’re not an England fan and we don’t want you.”
Rashford added: “I’ve grown into a sport where I expect to rad things written about myself. Whether it be the colour of my skin, where I grew up, or, most recently, how I decide to spend my time off the pitch.
“I can take critique of my performance all day long, my penalty was not good enough, it should have gone in but I will never apologise for who I am and where I came from.
“I’m Marcus Rashford, 23 year old, black man from Withington and Wythenshaw, South Manchester. If I have nothing else I have that.”