The Fir Park side were knocked out of the tournament by Aberdeen on Tuesday night, and now only have one competition left to compete in.
The defeat was a financial blow, too, since the manager Stuart McCall had hoped that a lucrative cup run would improve his budget for next season. Up to 11 players are out of contract in the summer and discussions have yet to start on extending any of those deals, or even to ascertain which players want to stay and which want to leave. Earning a second consecutive place in Europe would go some way to reducing the impact of a clutch of players leaving in the summer.
"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, who is one of the players out of contract in the summer. "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. You want to clinch European football as when I arrived I went straight into a side that was playing in the Europa League.
"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."