Pant, 21, has so far had a forgettable Caribbean tour, managing scores of 0, 4, 65, 20, 0 in the T20 and ODI series, though India won both the rubbers.
In the third ODI on Wednesday, Pant threw away his wicket while trying to send Fabien Allen out of the park, only to see his mistimed hoick land in the hands of Keemo Paul in mid-off. What made the dismissal look worse was that it came off the first delivery that Pant faced.
"Enough of babysitting the babysitter. Teach him the value of a wicket with some punishment," a fan wrote on Twitter.
"Rishabh Pant is throwing away the wickets .. what an overrated player," wrote another fan.
In comparison, batting at No. 5, Shreyas Iyer showed much more composure for his 41-ball 65, thus putting more pressure on Pant for a chance in the crucial No. 4 slot.
Batting great Sunil Gavaskar had recently backed Iyer over Pant for the number four position in ODIs.