United are looking to inflict more misery on the Lanarkshire side on Wednesday night when the Clydesdale Bank Premier League's bottom club visit Tannadice. Accies have not won since October and have not triumphed at home in the league all season.
"They finished brilliantly last season but what people forget is they have lost their best players," said Houston. "They have lost a couple to the Premier League, they have lost Simon Mensing to injury, who is a big player for them, and Alex Neil, and Mark McLaughlin has been out injured a few times, as has David Elebert."
Reid was subject to abuse from supporters when United triumphed at New Douglas Park in the Scottish Cup earlier this month and Houston was there again on Saturday when Accies were booed off the park at half-time during their 2-0 defeat by Hearts.
"That's where I feel a bit for Billy, he has had to let players go because the club need money like any other club," Houston continued. "That's something the Hamilton fans have got to recognise and give Billy and his young players a chance."
"Also, when you have your best players out long-term - and Alex Neil comes into that category - you have to blood young players, and young players take time to develop in the SPL.
Reid believes his Hamilton side can prove their critics wrong, beginning with Wednesday's fixture when they play their game in hand on 11th-placed St Mirren.
He said: "We've got a lot of work to do and with everyone starting to write us off I'm quite happy with that. Every game is a cup final for us at the moment. We need to try and take points in every game.
"We're capable of doing it - we haven't had the best of seasons so far, but that can turn. It's a game other teams will be looking at us and hoping we fall by the wayside.
"It's a place where we've done fairly well in recent seasons. We can go there and get a win."
Source: PA
Source: PA