The Hoops are still reeling from one of the worst results in their 122-year history, one which also left them facing a first trophyless season for seven years.
Saturday's limp loss at Hampden is a huge blow to caretaker-boss Lennon's hopes of succeeding Tony Mowbray on a permanent basis but striker Rasmussen is continuing to back the former Celtic captain.
Asked if the Northern Irishman should be kept on, the 25-year-old said: "Yes, I think he's great, I like him as a coach but it's not my decision."
A livid Lennon locked his players in the dressing room for 15 minutes after Saturday's game, telling them some of their Celtic careers were all but over.
Rasmussen, whose six-minute cameo at Hampden spared him most of the blame for the defeat, said: "Of course the atmosphere in the dressing room was not good.
"The players are disappointed because we know we didn't perform."
Team-mate Georgios Samaras was not so lucky, Lennon singling out the Greek and fellow forward Marc-Antoine Fortune for not being brave enough in front of goal.
But Samaras could count himself unfortunate with one shot that was deflected onto the post while it was still 1-0.
He said: "I did my best. I think the defender and the keeper both got a touch but I did the right thing. I was a bit unlucky.
"It was a poor performance and, at the end, we deserved to be out of the final. There are no excuses."
Celtic must now pick themselves up for tomorrow night's Clydesdale Bank Premier League game against Motherwell, which they cannot afford to lose if they are to deny Rangers the chance to wrap up the title before the split.
Fearing fans will vote with their feet at Parkhead, Lennon said: "Whether people turn up for that one is another thing, because I know how disappointed the fans will be.
"The majority of them will probably stay with us, but the players don't deserve that."
Opposite number Derek Adams urged the watching media to ensure Irn-Bru First Division County were given full credit for a richly-deserved win, the greatest result in their 81-year history.
He said: "That's up to journalists and media to point out that we were the better side over 90 minutes and to point out that we won 2-0 after 90 minutes; to point out that we had a clean sheet after 90 minutes.
"It doesn't matter who Celtic are; it matters that it was 11 against 11 on the park.
"We've won 2-0 and that's the respect that we should be shown."
Victory in next month's cup final against Dundee United would put County into Europe for the first time, something they would achieve regardless of the result if their opponents finish second in the SPL.
They also still have a chance of promotion to the SPL but probably need to win all of their four games in hand in a hectic run of fixtures, starting at Morton.
Adams said: "We've done very well this season and we don't have the budget that other clubs have.
"I would love to have the budget they have and I'm sure one day our football club will have that."