Boothroyd said: "I thought if we lost or drew the game we were out".
The Young Lions boss has been getting advice from his predecessor and senior chief ahead of his kids' "must-win" clash with Slovakia.
With only the three group winners, and best runner-up, progressing, Aidy Boothroyd's side have very little margin for error against the group A leaders, and Slovakia boast substantial quality in Sampdoria's centre back, Milan Skriniar, and Nordsjaelland's midfield player, Stanislav Lobotka.
Slovakia, who topped a qualifying group including Holland, came from behind to beat hosts Poland 2-1 in Lublin on Friday night.
Ward-Prowse was also captain for the Under-21s under Southgate - who gave the 22-year-old his senior debut in March - and revealed Southgate has been helping to guide the squad.
"It's great if I have any questions about players - Gareth can be my sounding board because he knows them all so well and was a victor with them in Toulon previous year".
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"I thought in the first half we had lots of possession, we controlled long periods but we didn't really hurt them apart from a few long shots and a couple of crosses".
"I've got to say, Abraham was very good", Pearce said on Sky Sports.
On the balance of play, Boothroyd's men were good value for the vital win, but the strong second half showing should not cover up just how poor the Young Lions were before the break.
"I think the response of the players in the second half is the important thing", the manager said.
"I have got nothing but thanks for him".
"It helps me to have a sounding board". It seems to happen every summer [that Southampton lose their manager] but that is the way football is sometimes. "The club and the players have shown that we can cope with managers and players going".