The Steelmen currently sit third behind Celtic and Inverness but are out of both cup competitions which leaves them to go about their league obligations without any other worries.
Goalkeeper Randolph says it is paramount for the Fir Park club to give everything and grab themselves a Champions League qualifying position come season's end.
"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."