Norris said he deeply regretted his actions following his celebration
Ipswich midfielder David Norris has been fined £5,000 after admitting a charge of improper conduct over a goal celebration at Blackpool on 8 November.
The 27-year-old had already been fined two weeks' wages by Ipswich for making a private message to jailed former Plymouth team-mate Luke McCormick.
Norris later apologised but denied it was a 'handcuffs' gesture.
The fine will be paid to the charity set up by the Peak family. Norris was also warned over his future conduct.
A Football Association regulatory commission statement said: "This was an act of immense naivety by Mr Norris, who should have considered the possible implications of his actions.
"However, we have also considered the subsequent actions by Mr Norris in not only writing to Mr and Mrs Peak but by personally meeting the family to apologise for his behaviour.
"The commission accepts the explanation of his gesture and that the remorse shown by Mr Norris to be genuine during the very sad time for Mr and Mrs Peak, who were also very gracious in accepting the apology from Mr Norris."
The player's actions initially angered the Mr and Mrs Peak after their children, Arron, 10, and Ben, eight, were killed when the Range Rover driven by McCormick, crashed into their car on the M6 in Staffordshire in June.
McCormick was sentenced to seven years and four months in jail for causing death by dangerous driving.
Norris wrote a letter of apology to parents Amanda and Philip Peak and later visited them in person at their Greater Manchester home.
The Ipswich player is available to face Sheffield United on Saturday, but is doubtful after picking up a dead leg in the 2-0 win over Derby last weekend.
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