Tuesday's 2-0 reverse to the Dons could have implications on Motherwell's budget for next season, but Randolph believes finishing in a European qualifying spot will soften the blow.
Randolph is one of 11 players out of contract at Fir Park in the summer and he is keen to leave the club on a high note, if he has to leave.
"We are out of all competitions but want to concentrate on the league and try and finish second and clinch a European spot," said Randolph.
"You want to do it for yourself and for others if it proves to be the case that this Motherwell team will break up at the end of the season.
"That would be a great achievement if this team is to break up and I guess it would be the way to bow out and give the club a parting gift by leaving on a high and clinching European football.
"Finishing as high as possible is the only thing left for us now and it does not make the Scottish Cup defeat to Aberdeen any easier to take as every club wants a good cup run. It is done now.
"We want to try and win that second place and that is what we have to look forward to. It is the next best thing and it is all we can do."