Albion sacked their head coach Clarke and his assistant Kevin Keen on Saturday following a 1-0 loss at Cardiff, which was their fourth straight defeat.
The midlands outfit are currently 16th in the Barclays Premier League, two points above the relegation zone.
Their next four fixtures see them play Hull at home on Saturday, Tottenham away on Boxing Day, West Ham away on December 28 and then Newcastle at home on New Year's Day.
And looking ahead to those games, Reid, quoted by the Birmingham Mail, said: "We can't feel sorry for ourselves.
"We have the biggest few fixtures of our campaign - this period will define our season. (With) the form we're in at the minute we need to dig in.
"Make no mistake about it, we are in it. We are in a relegation fight with other clubs and we can't forget that."
In their statement announcing the news of Clarke and Keen's dismissals on Saturday, West Brom also said that joint-assistant head coach Keith Downing would oversee first-team affairs while the club "consider all available options" for a new boss.
And Downing looks set to be in charge of the side for the Hull game, with the Baggies having subsequently confirmed that he will be doing the pre-match media duties at a press conference at Albion's training ground on Thursday.
West Brom are not making any comment regarding who their new permanent boss might be, but a host of people have been linked with the vacancy since Clarke's departure, with one of the latest being Mauricio Pellegrino, the former Liverpool player and coach who is currently in charge of Estudiantes in his native Argentina.
And regarding the Baggies' search, Reid said: "The board have got it right with the last few appointments.
"Roberto Di Matteo got it and took us on to promotion (to the Premier League in 2010).
"Roy (Hodgson) took us to another level of mid-table safety and Steve Clarke gave us our best-ever Premier League finish (eighth, last season).
"It will need to be a top-class coach, which is something we've had over the last couple of years.
"I wouldn't have thought someone will come in and break it away because what we've been doing the last few years has been the right way.
"The board will hope the new man gives the players a lift and gets us some results."