Ofcom said Royal Mail published an improvement plan for last year, aimed at delivering 85% of first-class post on time and 97% of second-class post, but "this has not materialised".
Mr Strawhorne said: "Royal Mail must rebuild consumers' confidence as a matter of urgency. And that means making actual significant improvements, not more empty promises."
Ofcom's investigation found the company "breached its obligations by failing to provide an acceptable level of service without justification".
It said the actions taken by Royal Mail to try and reach its targets were "insufficient and ineffective".
The fine, Ofcom said, reflected the "harm suffered by customers" as a result of Royal Mail's poor service.
Citizens Advice said the postal service's track record was "woeful" but that the fines may not push the company to do better.
"When these failures are just an ordinary part of doing business, Ofcom's fine risks becoming another operating cost, doing little to encourage the company to improve its service," Tom MacInnes, director of policy at Citizens Advice, said.
"Missed post has real life consequences, with people left waiting for urgent medical appointment letters, legal documents and benefit decisions."