Poole, 17, made his debut for Manchester United in their 5-1 Europa League victory over Midtjylland.
He joined United in September, after just 17 appearances for Newport County, who signed him when he was released by Cardiff City's academy in 2012.
Slade was not in charge when Poole left but said: "You don't want to be losing that type of quality."
The former Leyton Orient boss added: "Occasionally one does get away because young players develop at different rates.
"But clearly a decision was made at that particular time and they got it wrong."
Wales under-17 international Poole joined the youth ranks at Newport and was fast-tracked to a first-team debut against Shrewsbury in September 2014 aged just 16 years and 94 days.
Poole joined Manchester United for an undisclosed fee, believed to be an initial £100,000 which could rise to £400,000.
"I cannot control what has happened in the past, before my time," said Slade.
"But, certainly, if I had been here as manager at the time - obviously the personnel has changed at that level since then as well - you would be wanting to know the reasons why it actually materialised a player in three or four years time has gone and come on as sub for Manchester United."