For all their possession, particularly against 10 men when home captain Martin Skrtel was sent off for a stamp on Harry Kane, they lacked the wherewithal to make their dominance pay in a lacklustre Group F encounter in Trnava.
Then England's Adam Lallana produced a hopeful shot which Slovakia goalkeeper Matus Kozacik should have saved. Instead, the ball trickled through his legs and into the net for a 1-0 win, leaving Allardyce punching the air on the touchline.
Hodgson must have been punching the television.
He often said Lallana would soon add goals to his game and here he was, in the last second of his 27th international, fulfilling his prophesy for another manager.
Helping the midfielder out was a keeper who was outstanding as the teams shared a goalless draw at Euro 2016 when Hodgson was criticised for making several changes to his lineup.
That game was held up as indicative of England's tournament failings, yet Allardyce on his debut as manager fielded almost the same group of players against the same side and won. Such are the fine margins football managers live by.
RIGHT FORMATION
He knows his task is to find the right formation for some obviously talented individuals. There were signs in the second half that with the introduction of Dele Alli, who failed to fire at Euro 2016, that England are moving in the right direction.
Captain Wayne Rooney clearly remains key to their chances.
Before the game, Allardyce said he had no intention of telling such an experienced international where to play and so the decision for Rooney to drop deep, as he also did under Hodgson at Euro 2016, was presumably the player's.
Rooney indicated that is where he can best serve the team, and Allardyce is according him the respect 116 caps deserve.
Rooney was still in primary school when Allardyce entered management but a hallmark of the England coach's 22-year seven-club career is his ability to get the best from older players.
At Bolton Wanderers, World Cup-winning French striker Youri Djorkaeff enjoyed a golden spell at a time when many pundits had written him off, playing until he was 36, while Ivan Campo and Jay Jay Okocha also flourished in their 30s under Allardyce.
So England's new man should not be underestimated. He may not like opera or read as many European novels as Hodgson, but his gruff exterior hides an intelligence rooted in an ability to get inside footballers' heads and make them play better.
The country has just seen the first evidence of what Allardyce may be capable of. The performance was not pretty, but as England's new maxim proclaims, the journey has begun.
(Reporting by Neil Robinson; Editing by Ken Ferris)
