The West Lothian club are looking to get to the final of the tournament for the first time since they won it in 2004 when they travel to Hampden Park on Sunday.
And with both Old Firm sides knocked out, the path to glory seems to have opened up further for all semi-finalists including St Johnstone and Hibs, who play at the national stadium on Saturday.
Martindale noted that defender Efe Ambrose, 32, who won several honours with Celtic and Hibs as well as enjoying success with Nigeria, and 34-year-old midfielder Marvin Bartley, who won the Scottish Cup and Scottish Championship with Hibs, are as excited as anyone in the Livi squad.
He said: "There are players in there who have been professionals for 10/12 years and I can see the excitement in them approaching a national cup semi-final, players like Efe Ambrose and Marvin Bartley.
"Ambrose has maybe been more fortunate than the rest of them but even now he doesn't shut up about it, he keeps talking about it.
"Marvin Bartley is into the last year of his contract next year and he is saying it could be his last opportunity to get to another cup final.
"Since the day I came into this club (I have seen) the memorabilia all about the stadium, you can see a lot of 2004, Stuart Lovell, the cup-winning captain.
"Taking the club to a cup final and having a fantastic opportunity to win a cup final would be unbelievable. It would be a great and a massive positive for the club.
"This year has been really tough although we have light at the end of the tunnel.
"For the fans to be able to embrace that and watch it on Sunday, I think it will be a fantastic occasion and I can only assume if we get to the final it would be even better for them."
Martindale has won eight and drawn twice – the last two games against Celtic – since stepping up from assistant to take over from Gary Holt in November following a 1-0 defeat by St Mirren in the Scottish Premiership.
The Buddies also won 1-0 against Livingston in Paisley on the opening day of the league season and Martindale is determined to address that record.
He said: "The last two games we have played St Mirren, they have beaten us 1-0 twice.
"Richard Tait scored a goal the first time round and on the balance of play a draw would have been a fair result but you know that in football you don't always get what you deserve.
"And at home it was a deflected Jake Doyle-Hayes' strike. So they have beaten us 1-0 twice and I want to put that right."