England are into the semifinals after another underwhelming performance against the Swiss.
"Every now and then surely there has to be some enjoyment in this job," said Southgate. "I love the players and sharing that moment with them.
"I can't deny when things get as personal as it has it does hurt. I don't think it is normal to have beer thrown at you. But we are in a third semi-final in four tournaments. We will keep grinding, keep fighting and keep enjoying this journey."
He also told BBC Radio 5 Live: "I took this job to try and improve English football, to give us nights like this.
"We continue to give people fantastic memories.
"Now we want to deliver one more thing - we have never been to a final outside England, never won a Euros, so there are two bits of history we would love to create."