Relegation was confirmed last Tuesday when Oldham put Pools down as they beat Yeovil.
But first-team coach Barron, who conducted the club's press conference yesterday in the absence of John Hughes who collected a two-game touchline back at an FA disciplinary hearing at Wembley following his touchline dismissal at Coventry last month, admitted the players have been down.
He said: "It's a shame there's nothing riding on the game, but at Christmas people didn't give us a chance of staying up, so at least we gave it a good shot.
"In an ideal world there would be something to play for, but it's happened and we have to get on with it and playing the game properly.
"No-one thinks it's unimportant - it is and it's about having pride. A good display could set us up and make it four games without defeat.
"Some people will say it doesn't matter, but it does. The fans were fantastic last weekend when they applauded the players off the pitch at the end and we hope for the game again.''
And he confessed: "It's been difficult in training, trying to get them to train without that feeling of disappointment hanging over us. It's hard for everyone, we want to put sessions on for them to enjoy and learn from. It's been a case of talking to them and saying we need to keep going.''
Hughes was sent to the stands at half-time by referee Fred Graham at the Ricoh Arena after asking the official why he allowed Coventry's goal to stand after what Pools felt was a foul on Peter Hartley in the build up.
Graham reported Hughes to the FA and, after being charged, he requested a personal hearing. Yesterday's outcome means he will be in the stands at Crawley tomorrow and also for Pools' first game of next season.