Southgate's side take on the Czech Republic in Prague on Friday before facing Bulgaria in Sofia on Monday.
Chelsea striker Tammy Abraham said earlier this week that England could leave the field if there is any repeat of the sort of abuse directed at England's black players during the qualifier in Montenegro in March.
However, Southgate insisted they will follow UEFA's three-step protocol that ensures the crowd are warned the match will be suspended if racist chanting is not stopped.
"There is a UEFA process and we have to have faith in that process," said Southgate.
"Everything else is hypothetical as we don't know the situation we will be in as a team or I will be in as a manager."
Earlier on Thursday, president of the Bulgarian Football Union (BFU), Borislav Mikhaylov, had branded suggestions England would be forced to take such action as "derogatory".
"I strongly suggest that the UEFA administration take measures against the build-up of unnecessary tension," Mikhaylov said in a letter to UEFA published online.
"The Bulgarian public has in no way committed any recent infringements that deserve it to be stereotyped as 'racist' or 'hostile'."
However, Southgate explained that he had simply prepared his players for any eventuality after the abuse they suffered in Montenegro in March.
"Inevitably, because we suffered a situation in Montenegro we wanted to be clear what might happen if something happened in the future. We are very clear on that," added Southgate.
"We want the players to be able to concentrate on football, they want to be judged on football.
"What I've got to do is provide a secure, safe environment for them to play."
Sterling has 'full faith' in UEFA
Raheem Sterling was also the subject of racial abuse when England beat Bulgaria 4-0 at Wembley last month.
The Manchester City forward has been an outspoken campaigner on the need to do more to eradicate racism from the game.
However, Sterling said he still has "full faith" in UEFA's handling of racist incidents.
"As a player, with the situation that happened in Montenegro, I don't think as a team we were quite prepared and knowing there was a protocol in place," said Sterling.
"As a team, we had a meeting and Gareth sat us down and explained there was a UEFA protocol.
"Now as players we have got to kind of give UEFA a chance to take that responsibility on board and deal with that situation.
"At this moment in time, full faith in UEFA."
The game will be England's first visit to Bulgaria since September 2011, when Ashley Young was subject to monkey chants as the visitors won 3-0.
The BFU was fined 40,000 euros ($44,000) by UEFA for "discriminatory" chanting and because fans threw fireworks.
Bulgaria were also punished by UEFA for "racist behaviour" when they lost away to the Czech Republic on June 7 and at home to Kosovo three days later in Euro qualifying.
For the England visit, UEFA has ordered the BFU to close at least 5,000 seats at the Vasil Levski National Stadium and display a banner that reads: "#EqualGame".