England drew 1-1 with Hungary when John Stones's header equalised a penalty given away by Luke Shaw, and with Poland winning in Albania, they need four points from their final two qualifiers to secure their place at the Qatar tournament.
With more than half a game to chase a winner against a Hungary side that did not take many risks, they seldom looked like doing it.
It was not a great advert for the more positive 4-3-3 formation many fans have been clamouring for, with Phil Foden and Mason Mount playing as more attacking companions to Declan Rice than his usual sidekick, injured Leeds United midfielder Kalvin Phillips.
Southgate abandoned the plan and brought off Kane and Raheem Sterling with 15 minutes to go as he switched to 3-4-3.
"I think we had one or two tactical problems we managed to resolve as the game progressed but some of our quality was just really poor," said the former Middlesbrough captain and manager. "We gave unusual passes away, we got caught in possession several times, we overran the ball several times, we forced things a bit too often.
"We started the game that way and that, I thought that bred a little bit of anxiety in our play, which is quite unusual.
"We still had over 60 per cent possession so we were still generally controlling the game but we didn't really get much pressure as much onto them, certainly as we did in Budapest (in the reverse fixture).
"Again, I thought that meant some of their counter-attacks we weren't in the right position on transition and they brought a bit of anxiety.
"Having gone behind I thought it was a good response to draw level but I don't think we did quite enough to win the game even though we had more shots, more possession. I don't think we created the really clear chances."
Of the different tactical set-up, which saw Jordan Henderson only a substitute despite being a more direct replacement for Phillips, who had a minor calf strain, Southgate added: "I think we've been playing 4-3-3 a lot but perhaps with a different profile of No 8s. We wanted to look at something a little bit different.
"We didn't have Kalvin Phillips anyway who's been such an essential part of that midfield and we knew we would have to break a packed defence down. I'm not certain it was the profile of the players that was the issue in terms of not being able to break them down.
"We just didn't play with the same fluidity and individual level of performance we've come to appreciate and expect and I think we have to be honest about that as a group."
Southgate's opposite number Marco Rossi was in belligerent mood, but accepted his team had caught the Three Lions on an off-night.
"The guys followed the tactics from the beginning to the end and brought their skills and their heart," he said.
"We found an English team that was not properly at its best.
"After the last match against Hungary I was an idiot and it was hard to accept this. If you win a match you are a hero, if you lose you are an idiot.
"But three months ago Hungary played an unbelievable European Championship. I said to qualify for the World Cup was a dream and we are out of this now but we are not the idiots some of our supporters were saying."
Understandably, neither Southgate nor Rossi were prepared to comment on crowd trouble during the game, which they were not fully aware of at the time.
Fighting broke out when a Hungarian fan was arrested for allegedly racially abusing a steward. Hungary were punished for crowd trouble when the sides met in Budapest in September's reverse fixture, and both countries were penalised for the behaviour of their fans during European Championship home games.
A flare was also let off in the away end after Roland Sallai converted his penalty. That it was let into the crowd could be a problem for England, who are still waiting to discover their punishment for the disgraceful scenes around the summer's European Championship final.