The Caribbean outfit were chasing a target of 204 for a consolation victory in the three-match series but capitulated in spectacular fashion at Sabina Park in Jamaica.
The total was just one run better than New Zealand's Test-record low of 26, set in 1955, but it was 20 runs short of West Indies' previous worst total of 47.
"It's disappointing," Chase said after the game. "We've been putting ourselves in positions to win games, and then we just lay down and not put up a fight in the last batting innings.
"It's quite heartbreaking, because I think we did it in all three Tests, and we're not really learning from our mistakes. So that's something we have to really look at.
"Obviously being bowled out for less than 30 is quite embarrassing."
The record low total was indicative of the series with the bat for the West Indies, having posted scores of 190, 141, 253, 143, 143 and 27 across the series.
Chase conceded that the Carribean outfit faced a huge task to rebuild in the longest format with their next Test series scheduled against India away from home in October.
The skipper added: "We need to really take a deep look at ourselves as batters. The next series from here is quite a while. So we have time on our side.
"So I think that's what we need to really do, really have a look at our batting this series and see where we can improve and how we can put 300 run totals on the board.
"Obviously India is going to be different conditions, probably more spinner-friendly. So I think if you can have some batting camps around playing spin bowling and stuff like that, I think that will be ideal for us going into those conditions."
The West Indies cricket board (CWI) has sent invites to a trio of legends - Brian Lara, Clive Lloyd and Viv Richards - to take part in an emergency meeting following the Test series defeat to Australia.
West Indies clawed their way back into the pink-ball Test at Sabina Park on Sunday, reducing Australia to 99 for six at stumps on day two.
Spinner Nathan Lyon was left out of Australia's Test team for the first time in over a decade for the third Test against the West Indies in Barbados.
Day one of the Third Test belonged to the West Indies, as their pace attack dismantled Australia under the Sabina Park lights, triggering a dramatic collapse that saw the visitors slump from 129 for 2 to 225 all out.
