With a top seven finish still within reach, the visitors were on the front foot for much of the first-half as Hallam Hope went closest to breaking the deadlock.
The United striker forced Stuart Nelson into a second smart save early after the restart before Alex Dobre almost converted against the run of play.
Ending brightly, Alex Pattison, Jake Gray and Ryan Seager all went close to snatching victory late on but it was to be a share of the spoils in an afternoon that saw the club’s 16-year league status come to an end.
Unable to beat the drop last weekend, Neale Marmon was forced into two changes for the club’s final EFL fixture before starting next season in the National League.
Loan goalkeeper Nathan Baxter has made his last appearance for the green and whites with a small niggle ruling him out of a home goodbye, as veteran stopper Nelson came in between the sticks.
Suffering with a shoulder problem, Sessi D’Almeida also dropped from the squad to see Alefe Santos take his place whilst four academy products were named amongst the substitutes – the most at any point this season.
Able to look to the future with nothing riding on the game, it was a different story for Steven Pressley’s side who needed a win to keep their faint play-off hopes alive.
With that in mind, the Cumbrians were quickest out of the blocks and tested Nelson twice inside the opening 10 minutes.
Town’s number one stood tall to parry away Hope’s stabbed strike from 12 yards, before comfortably collecting Nathan Thomas’ strike from range in a bright start for the visitors.
Maintaining their dominance of possession the Blues lost some of their attacking threat shown early on, as the game ticked to the half-hour mark with most of the action in the middle of the park.
Unable to penetrate a resolute looking Yeovil defence – led mainly by an imperious Bevis Mugabi – Carlisle were forced to try their hand from range as Mike Jones and Stefan Scougall both failed to test Nelson further.
Struggling to enjoy any territory or possession the Glovers remained on the defensive, but managed to keep it goalless at the halfway stage.
Feeling very much like an end of season encounter in sunny Somerset, Carlisle started the second half with the kind of tempo you’d expect from a side still in with a chance of reaching the play-offs.
Thomas again fired into the arms of Nelson before an almost carbon copy of Hope’s early chance in the first-half.
Played in by Mike Jones’ ball over the top, United’s top scorer was again denied by Town’s stopper who had raced from his line to reduce the angle and block well.
Yet to register a shot on goal, the Glovers almost stunned the visitors by netting with their first chance of the match.
In a rare foray forward, Courtney Duffus’ cross found strike partner Dobre whose dipping header was acrobatically tipped over the bar by Adam Collin.
After a flurry of action at both ends of the pitch the game resorted back to a defensive battle, as the chances dried up for both teams.
Continuing to work the ball into promising situations, Pressley’s side were unable to force the best out of Nelson who looked comfortable.
Having ridden the storm defensively, the green and whites looked to end what had been a campaign to forget on a high with a bright spell late on.
Dobre’s cross came all the way through to Pattison 10 yards out, but his stabbed strike lacked the power to beat Collin before Tom James glanced a Gray corner into the side netting moments later.
After teeing up James, Town’s midfielder almost grabbed his third in as many games but for a superb double save from Collin.
Racing onto Alex Fisher’s cross, Gray saw his curling strike parried straight back to him only to see his venomous volley once again kept out by Carlisle’s ‘keeper.
Finishing with a flourish there was only one side looking likely to break the deadlock late on and substitute Seager almost did just that.
James’ wide free-kick delivery was glanced towards goal by the Yeovil-born striker and was destined for the far corner but for Collin’s full-stretch dive.
Proving to be the final chance of the match it was to end in a third successive draw for the Glovers, who headed into the afternoon with relegation to the National League already confirmed.
Yeovil Town: Nelson; Worthington, Sowunmi, Mugabi, James; Gray, Santos (Arquin 70′), Pattison, Abrahams (Seager 76′); Duffus (Fisher 80′), Dobre.
Bookings: Pattison 24′, Gray 88′.
Subs not used: Scott, Ojo, Rogers, Arnold.
Carlisle United: Collin; Liddle, Gerrard, Parkes, Miller; Jones, Slater (Cullen 71′); Thomas, Scougall, O’Hare; Hope.
Bookings: Gerrard 69′, Jones 77′.
Subs not used: Gray, Kennedy, Devitt, Glendon, Gillesphey.