Mulgrew, also voted the season's best player in Scotland by his fellow professionals, has enjoyed a memorable campaign having won his first Scotland cap in a friendly against Slovenia in February.
But the defender admits to a tinge of regret after his side's hopes of a domestic treble of trophies came to an end with a League Cup defeat by Kilmarnock while Sunday's opponents Hearts knocked the Glasgow giants out of the Scottish Cup at the semi-final stage.
"Winning the cups would have been nice after getting to a semi-final and final but we'd have taken winning the league at the start of the season," Mulgrew said.
"We'll just need to look at the positives and improve next year again," Mulgrew said.
Hearts will try to ruin Celtic's title winning party at Parkhead by claiming the point that will guarantee fifth spot and European football.
Despite the likelihood they may rest several key players before next week's Scottish Cup final against Edinburgh rivals Hibernian, Hearts first team coach Gary Locke said there'll be no slacking this weekend.
Rangers will bring down the curtain on a season to forget with a game away to St Johnstone.
Their future is far from certain after entering administration in February, a move that saw them docked 10 SPL points, while preferred bidder Bill Miller pulled out of the process to buy the 140-year-old club earlier this week.
With Ally McCoist's side having already secured second place in the SPL there is little at stake for the Gers.
But Rhys McCabe says the match is far from meaningless and wants to win the match at McDiarmid Park as a thank you to the fans for their support following a difficult few months.
"Rangers are a big club and we owe the supporters a result for the backing they have given us," the midfielder said.
-AAP