The Storm will look to avoid a 14-year low of five straight losses when they travel to Canberra to face the Raiders.
With a 2-4 record to open the season, they are in unfamiliar territory, sitting 13th on the ladder, with only three teams conceding more points.
The No.9 agreed with the assessment that Melbourne's performance, and particularly defence, wasn't up to standard and said the team needed to "show more grit" when things weren't going their way.
But Grant felt talk of the Storm missing the finals was premature, and backed his team to work their way out of their current rut.
"We're six games into a 27-round season and the finish line's a long way away, so we've just got to keep improving and making sure we're accountable and we'll get our performance right," the Test hooker said.
"People can have their opinions, but that doesn't mean too much.
"We're eliminating all the outside noise - we've got the answers in the club here, we've got the answers with the playing group, with the coaching staff, but it's just about applying it."
Melbourne can take heart from some recent form reversals.
Friday night's opponents were in a similar predicament with four straight losses before last round's 36-34 win over South Sydney.
Last season Penrith lost five straight between round two and six but recovered to just fall short of a grand final berth.
"You can certainly take inspiration from other teams and where they've been and past Melbourne Storm teams have been in this position as well," Grant added.
"But at the end of the day it's a different team, it's a different environment and it's us that's in it and it's us that make it happen."
Young second-rower Joe Chan was in the firing line of coach Craig Bellamy during their 38-14 loss to the Warriors and was hooked not long into the second half.
Grant said Chan was still a "great asset" for the team.
"Everyone's been in those shoes at times as a player, and we just need Joey at his best.
"It's not one player, it's collective ... he's a great asset to the team so it's important that he gets back to that this week."
