Defeat against Australia in Cardiff on Sunday (Monday AEDT) would inflict an all-time low of 11 successive Test match losses.
Wales haven't won a Test since beating 2023 World Cup pool stage opponents Georgia, while Warren Gatland's overall success rate since returning for a second stint as head coach currently stands at less than 30 per cent.
To underline the size of Wales' task, Australia have won on nine of their last 11 Cardiff visits and are fresh from a scintillating victory over England last time out.
Jenkins has been in the Wales camp for almost all of the past 33 years, winning 87 caps between 1991 and 2002 and then returning as an assistant coach and kicking specialist two years later.
He has been there every step of the way with Gatland, including the New Zealander's first reign that featured World Cup semi-final appearances, Six Nations titles and grand slams.
"You want to win. And when you don't, you feel upset," Jenkins said. "You are desperate to be successful.
"It hurts. If I didn't care about it, I wouldn't be here, I can assure you of that.
"You have to get back on the horse with a tough game coming. We are more than capable of winning, and we've got to show that on Sunday."
Wales' demoralising run includes home defeats against Italy and Fiji, a Test series 2-0 loss in Australia and narrow reversals at the hands of Scotland and England.
Fiji's first away victory over Wales has ramped up the pressure on Gatland, who has found himself in a position of facing questions about his future from the media.
"He understands it," Jenkins says of Gatland. "It is common sense we are under pressure. I've been in here long enough as a player and coach.
"Gats has been his usual self. He works hard and keeps going - he understands the game inside out."
A number of front-line Welsh players have retired from Test rugby during the last 18 months - like Alun Wyn Jones, George North and Dan Biggar - while Louis Rees-Zammit went to the NFL and influential No.8 Taulupe Faletau has been a long-term injury absentee.
More than 20 players have been capped since Gatland returned, with that inexperience underlined by fly-half Gareth Anscombe having more caps than the rest of Wales' back division combined on Sunday.
"There are no excuses at the end of the day," Jenkins said. "We can probably hide behind that inexperience, but Test rugby is an uncompromising place.
"We know Australia are going to be a good side and full of confidence after winning at Twickenham for the first time in a long time.
"We are excited for the challenge. Whether we've lost eight or 10 on the bounce, Test football is about winning. We are more than capable of doing that."
