Marvin Morgan, who scored both Shrews goals, and Jermaine Grandison were allegedly subjected to racial comments by a section of the home support in the first half at Victoria Park.
A statement released by Town read: "Shrewsbury Town FC can confirm that Graham Turner and players Marvin Morgan, Jermaine Grandison and captain Matt Richards were called into the referee's room where discussions took place at half-time on Saturday regarding racial comments directed at the players.
"We understand the referee (Carl Boyeson) included the conversations in his match report to the Football League.
"The matter is now subject to a police and FA investigation and no further statements will be made."
Hartlepool did not want to comment on the incident when contacted.
An FA spokesman said: "We are aware of it and we are making enquiries."
(reopens) Hartlepool have since released a statement condemning alleged comments should they prove to be true and have pledged to assist in the FA's investigation.
It read: "Hartlepool United are aware of alleged racial abuse aimed at Shrewsbury Town players Jermaine Grandison and Marvin Morgan during the first half of Saturday's game at Victoria Park and have been asked by the FA to provide any further information we have concerning the incident.
"The club will do everything possible to help with any external investigation and we are currently carrying out our own internal investigation.
"The club would like to remind supporters that racism in any form will not be tolerated at The Vic, as the club have shown in its ongoing involvement in the Kick It Out campaigns.
"If any supporters do hear any abuse towards individuals of any nature the club requests that you to advise your nearest steward so that appropriate action can be taken.
"The club has no further comment at this stage."