The 25-year-old Argentinian was disciplined and also left out of the team for Tuesday night's Auto Windscreens Shield match at Chester City following an investigation by the Victoria Ground club.
Di Lella was accused of punching Morgan in the player's lounge after last Saturday's FA Cup second-round match at Craven Cottage, which Kevin Keegan's side won 4-2.
The Buenos Aires-born player was incensed and had to be substituted during the second half after suffering a cut eye, which he later claimed had happened when Morgan stamped on him.
"We have acted quickly in fining Gus and suspending him from [Tuesday] night's game, and Fulham are happy with what we have done," the Hartlepool manager, Mick Tait, said yesterday.
"Gus regrets what he has done and I don't think it will happen again. Something happened and he reacted wrongly.
"I am hoping the matter will now be forgotten and Gus can get on with his football. He has been made aware that we don't think what has happened is acceptable, and I am sure he has learned from this."
Tait was not present when the incident took place and launched the investigation after receiving correspondence from Fulham.
Hartlepool are now hoping that the Football Association will not feel the need to make the matter any further by levelling a charge of bringing the game into disrepute.
"I hope it won't come to that and that the FA will let the matter drop," Tait said. "The matter should have been dealt with internally and I hope the FA will be happy with what we have done."Reuse content