Widnes scored twice in the final seven minutes to come from behind to beat Rovers last Sunday.
Costigan admits his side should have defended better to seal the win which would have lifted them to seventh in the table.
As it stands, the Robins now travel to Salford in 10th spot knowing the Red Devils will leapfrog them with a win.
Costigan, who was one of just five players not to have missed a tackle against Widnes, insists improvements have to be made.
"If we want to beat Salford we'll have to get rid of those mistakes, especially in defence," Costigan told the Mail.
"Our attitude wasn't up to where it should have been.
"It's a team effort, but the individual efforts didn't help.
"There were too many one- on-one missed tackles which helped their half-backs to do what they wanted.
"Kevin Brown can do very special things on the pitch.
"The good thing about rugby league is that we have another game this weekend to prepare for.
"Salford will be another battle and hopefully we can get back to winning ways."
Kevin Brown had a great game against Rovers with a hat-trick which will have encouraged Salford's enigmatic playmaker Rangi Chase.
Costigan, a former State of Origin star for Queensland, doesn't want to see his side let slip a seven-point lead late in a game again.
Rovers surrendered a 20-point lead at Salford last season, but Costigan is confident his side have learned their lesson.
"Sunday was very disappointing," Costigan said.
"Leading by seven points with seven minutes to play, you should win. You don't have to do anything special to win.
"In future if we are in the same position, we have to get to our kicks and defend.
"We have to put the pressure on the other team and force them to throw the ball around and make mistakes.
"We didn't think that way against Widnes and it's very frustrating."
Costigan is determined to make Iestyn Harris' Salford side pay for those frustrations.
Salford are also licking their wounds from losing a lead with 17 minutes to play against Catalan.
The Dragons went on to finish the game strongly to win 37-24, the same score they beat Rovers by.
Costigan wants the Red Devils to feel the pain Rovers felt after their Widnes defeat.
"Hopefully we can make Salford pay for our disappointment against Widnes," he said. "We were hurting after the game and hopefully we can put some points on Salford, but we have to stop them from scoring points on us too."
KR prop Jonny Walker will miss the trip to Salford after being handed a one-game ban after entering an early guilty plea. Walker admitted a grade B dangerous contact offence on Widnes' Ben Kavanagh during Sunday's 34-29 defeat.
