Higgs told the club website: "Unfortunately heads are going down too quickly at the moment.
"We need the players to take on responsibility for our position and do something about it."
Former manager Paul Trollope was sacked by the Pirates in December last year, but new boss Penney has struggled since his appointment, with the side gathering just five points since his arrival in January.
The side have conceded 28 goals during that nine-game period.
We gave away stupid goals with three individual errors and saw ourselves on the end of another heavy defeat
Higgs on Bristol Rovers' defeat by Leyton Orient
But Higgs added: "Our season is not over - there is still time to turn this situation around and we can still stay in this division if we dig in and defend properly and cut out the simple errors which are costing us points week in and week out."
Penney's side recorded their 15th league defeat of the season at Leyton Orient last Saturday, and Higgs said the side have to start cutting out basic errors.
"Yet again, we gave away stupid goals with three individual errors and saw ourselves on the end of another heavy defeat, " Higgs continued. "At 2-1 down we were still in with a chance, but more sloppy defending cost us dearly."
Higgs also confirmed that there was no reason why the side would enter administration should they fail to escape relegation to League Two.
He said: "There is no fear of the club going into administration whatever division we play in.
"We are all in this together and if we pull in the same direction, we still have every chance of getting out of this mess."
Source: BBC Sport
Source: BBC Sport