The stuffed Lions that travelled with the team during their ill-fated Euro 2016 campaign have been consigned to storage but as Allardyce reflected on Adam Lallana's 94th-minute winner in his first game as national boss, he held a newly-acquired memento in his hand.
"I got this lucky penny off a lad today in the hotel," he explained.
"A father and his son in a wheelchair came to the hotel this morning and asked if it was okay to have a picture. When we finished he said: 'Let me give you a lucky coin.' Here it is. I had it with me in my pocket, we won, so it'll stay with me.
"I'm not really superstitious but I'm going to keep it. It's got us a last minute winner. I wonder how far it will take us."
What would have become of the coin had Lallana not swept home his first international goal with virtually the last kick of the game is uncertain.
But while that goal gives Allardyce three crucial points, as much for their symbolic value as their usefulness in a World Cup qualifying group England should navigate with relative ease from here on, it did not paper over every crack.
Allardyce's England might have gone one better against Slovakia than Roy Hodgson's team managed in June, when they laboured to stalemate in St Etienne, but problems still linger as they left it late to break down opponents reduced to 10 men after Martin Skrtel's 57th-minute sending off.
Harry Kane is not currently the domineering number nine England need and want him to be, Raheem Sterling did not bring his Manchester City form with him to Trnava and Jordan Henderson failed to take his chance in the centre.
But most pressing is the role of captain Wayne Rooney.
On the occasion of his 116th cap, breaking David Beckham's outfield record, he was surprisingly asked to perform a deep-lying midfield role.
Hodgson used him similarly throughout the Euros but the experiment appeared to be at an end after Jose Mourinho restored him to an attacking position at Manchester United.
Allardyce declared himself happy with Rooney's performance but curiously suggested that he had deferred to his skipper over where he played and even expressed surprise at how far he dropped.
"Today Wayne played wherever he wanted to. He was brilliant and controlled midfield. I can't stop Wayne playing there," said the manager.
"I think that he holds a lot more experience at international football than me as an international manager.
"Yes he played a bit deeper than he does at United, but Wayne's comfortable, when I talk to him, about the position.
"This is the most decorated outfield player in England. He's won everything at Man United, more or less, and at Champions League and domestic level.
"Using his experience with a team, and playing as a team member, it's not for me to say where he's going to play. It's up to me to ask whether he's doing well in that position, and contributing.
"If so, great. We'd like to get him into goalscoring positions more. He's been a goalscorer all his life and I want him to do that again, but he reads a game as he reads it. He read it very well, we won the game and dominated the game, outplaying the opposition.
"I must admit, he did play a little deeper than I thought he'd play today, but I was pleased with his performance."
It is unlikely to be the last we hear about Rooney's place in the team, or his apparent influence on Allardyce's tactics.
For now, though, he is able to look back on an exciting start, and a winning one, in his dream job.
"It's the biggest job I've ever had," he said. "You know you're leading the nation forward. Everyone is looking at you. They want you to show the way forward and be successful and it's that much bigger when the nation's watching you.
"I had a whole lot of messages today. It was impossible to try and attempt to reply to all the goodwill messages from across the country. In the end, everyone back home was waiting with bated breath and we scored the winner.
"Everyone back home is happy and can have an extra drink. The fans here were happy and the goal came in their end. We dominated the game and finally got what we deserved.
"The result did us justice in the end."