Livi have again exceeded expectations by reaching the Betfred Cup final and securing top-six football but their Hampden conquerors, St Johnstone, have overtaken them for fifth spot in the Scottish Premiership.
David Martindale's side need to beat the Saints in Perth on Saturday to move back into fifth and give themselves a chance of a place in European football.
Fifth spot would seal a place in the Europa Conference League qualifiers if Hibs were to beat St Johnstone in the Scottish Cup final and Livi succeed in an appeal over their rejected UEFA licence.
Mullin said: "It's exciting going into the last game of the season having something to play for. Obviously we would have liked to have had that wrapped up a few weeks ago but it wasn't to be.
"If anybody had offered the boys top six and thrown in a cup final, you would have bitten their hand off for that.
"It's been an excellent season but it would be nice to finish that off with a win on the final day to secure fifth and build that momentum for the start of next season."
Livi have lost all four games since the split.
"We have done so well for a massive period of the season so we don't want to let it just fizzle out as if we have taken our foot off the gas," Mullin said.
"That's not the case at all, results just haven't gone our way.
"You need to remember we are playing the top teams in the league. Things like silly goals have gone against us so we will be looking to finish on a high."