Paul Horton has described the prospect of reigning champions Lancashire being relegated from Division One of the County Championship as "criminal".
They lie third from bottom, having won just one of their first 11 matches.
"We've got five cup finals left in four-day cricket. If we can win a [one-day] trophy, we'll probably be happy."
Sydney-born Horton, 29, added: "If we win three or four of those games, we'll definitely stay up.
"A lot of the sides that we play are around us so our destiny is in our own hands."
The first of those remaining five matches, against Somerset at Aigburth, starts on Wednesday.
In contrast to their record in the longer format, Lancashire's one-day form has been exceptional.
A four-wicket win over Gloucestershire at Old Trafford moved the Red Rose to the top of their group in the CB40 competition and in a strong position to reach the semi-finals.
"There are three trophies up for grabs and if you can win one of them, you've done well," said Horton.
"All sides set out to win three trophies. Things pan out that you play better and things fall for you in certain competitions.
"Last year, things fell for us in the Championship, we got momentum and we played some good cricket.
"It hasn't worked out as such in this campaign. We've played 11 games in the bad weather, we've played some poor cricket at times and sides have won games against us."