Having opened Group B with a stunning 6-2 victory against Iran and then drawn 0-0 with the United States, last year's Euros runners-up are well placed to reach the World Cup last 16.
England will progress so long as they avoid a four-goal defeat to Wales, whose manager Robert Page appeared to write off their hopes after the late 2-0 loss to Iran followed their 1-1 draw with the US.
Their chances of reaching the knockout phase may be hanging by a thread but Southgate knows Tuesday's opponents will be desperate to secure a first World Cup win since 1958.
"We have got to play well," Southgate said ahead of the Ahmad Bin Ali Stadium showdown.
"We are going to play an opponent that is wounded and, like everybody else, desperate to beat the English. We know what that will be.
"We have got to play an intelligent game and play well. Match the spirit.
"I would be very disappointed if someone says to me that their players will want it more than ours.
"I would be asking questions about what we stand for and what we have been for five years. We are not quite done.
"We need a point more to be certain of qualifying. We need three points and if we get that we top the group and I don't think many groups will be topped with nine points."
Southgate stressed the need to use the ball well and make sure they step up on the US stalemate, meaning they will analyse their selection options over the coming days.
Tuesday's match is likely to come too soon for James Maddison having only started training on Saturday following a knee complaint, while the likes of Alan Shearer have suggested Harry Kane needs a rest.
The England captain underwent a scan on his foot after a poor challenge against Iran and completed Friday's draw with the US, with Southgate baulking at the suggestion playing him was a risk.
"No gamble at all," he said. "He has had a whack to his foot so there is a tiny bit of discomfort when he is striking the ball but we are not talking about anything that was a risk in any way shape or form."
The next few days may feel similar to last summer, when an impressive win against Croatia in their Euros opener was followed by a drab goalless draw with Scotland.
There was a smattering of boos at the end of that game at Wembley, just as there was in Qatar on Friday evening.
Southgate questioned whether they were aimed at England but knows the stalemate will only add to this "tournament of external noise".
"I have been in lots of tournaments as a player," the 57-cap former international said.
"I remember in 1998 when we beat Tunisia and then lost to Romania and I remember saying to the players after that if anybody thinks we can't beat Colombia, then what are we doing.
"You have to go three games. You have got to be ready to do that.
"We are going to go to knockout games eventually anyway so you have got to be able to handle those moments.
"When you have had as much flak as me you are not really bothered about having a bit more."