Smith was sacked as manager of Boro on Wednesday after 14 months in charge following a run of 14 defeats in 18 games.
Skipper Roberts - who had a brief stint as caretaker before Smith replaced Graham Westley at the club - has been placed in temporary charge while the board search for a replacement, and he has challenged his players make up for their dismal recent form.
"It's a massive disappointment for Gary and the management team to be leaving the football club because they were doing a lot for positive work for the team," he told Stevenage's official website.
"They've put a lot of positive things in place and brought a lot of players to the football club that will bring success in the future.
"For one reason or another it hasn't worked out, and I think as players we have to take a huge part of the responsibility for that.
"I think the players, on too many occasions, have let the management side down and we're fortunate that we're the ones who remain at the football club so it is up to us to show what we're all about for the rest of the season, to show a lot of character and that fighting spirit and I'm sure that'll start on Sunday at Tranmere."
"This season we started off on a tremendous run of form and took to the league very well - to go second in League One was another huge achievement. A third of the season had gone which showed it was no fluke, but for one reason or another we haven't been able to see it through and maintain that and we have been searching for that form ever since.
"We have shown flashes of it in recent weeks and that character and level of performance is what we need to show in the seven games that remain this season.
"As captain it is up to me to lead the dressing room and make sure that we get the very best out of ourselves. When I am in charge it's no different, it's all about leading by example and getting the best of your ability and that is what I'll ask from the lads."