With the experienced Shakib-ul-Hasan starting his six-month suspension for "serious misbehaviour", the pressure is on the rest of Mushfiqur's squad to end their 50-over nightmare in Grenada on Wednesday.
The minnows are yet to win an ODI this year, but travel to the Caribbean knowing their best record against a Test playing nation - apart from Zimbabwe - is against their hosts.
Bangladesh won their last ODI series in the West Indies 3-0 back in 2009, and Mushfiqur has challenged his team to repeat that success.
"He [Shakib] is a big performer and has been a great contributor for the last eight years, but it isn't as if we were all relaxed when he was there," Mushfiqur said.
"Cricket is not a one-man game - we need at least three to four players to perform in our team, so from that aspect we are motivated that many players who haven't been in form have been working hard.
"Hopefully they can motivate themselves to work harder. They need to put in their best performance."
Bangladesh's performances in their recent ODI tour of India showed some promise, with Taskin Ahmed and Mashrafe Mortaza leading their attack well with impressive spells of fast bowling.
Imrul Kayes and Rubel Hossain have returned to the Bangladesh squad for the series and could feature as they bid to recapture their form.
Rubel was dropped for the recent matches with India but remains their highest wicket taker in the calendar year, while Kayes provides further options at the top of the order but may not play after Tamim Iqbal struck 91 in their warm-up match.
Meanwhile, West Indies captain Dwayne Bravo will hope his side can bounce back from their 2-1 ODI series defeat to England in March.
Bravo has returned from a shoulder injury to lead the team, while Chris Gayle, Kieron Pollard and Kemar Roach are also likely to play following their recalls.