Basement boys Bradford had suffered six straight league defeats before ending that sorry run with a point at London Road.
Anthony O’Connor gave the visitors the lead 10 minutes in before former Barnsley boy Ivan Toney equalised just after the hour.
After seeing the video replay, Hopkin was certain Toney was offside.
He said: “I’m disappointed we’ve lost two points. I’ve seen the goal on the video and he is off – the linesman is nowhere near him.
“But if somebody had said before the game we’d get a point at Peterborough, we would have taken it. In months gone by, we’d have probably gone on and lost it. So, from that perspective I’m delighted.”
The Bantams’ fast start kept Posh goalkeeper Aaron Chapman busy.
Debutant and free agent Paul Caddis tested him with a curling effort before Huddersfield Town loanee striker Jack Payne’s attempt was kept out by the goalkeeper’s legs.
But O’Connor’s effort was too good for him as Bradford deservedly took the early lead.
Defender O’Connor slotted home his fourth goal of the season to become the club’s joint leading scorer after being found in the area by Hope Akpan.
After going ahead, the Bantams had to defend their lead resiliently against League One’s top scorers.
Steve Evans, who has never been on the losing side as a manager against the Bantams, saw his side throw everything at the visitors after the break.
Half-time substitute Toney fired them level in the 61st minute after being played in, leading to Hopkin and his assistants venting their feelings on the sidelines as the officials failed to give offside.
The Peterborough pressure kept coming but the Bantams’ backline held firm and right at the death Payne and Lewis O’Brien pulled off timely blocks to secure a point and saw the Posh slip to fourth.
Peterborough United: Chapman, Naismith (Dembele, 45), Tafazolli, Bennett, Denton, Woodyard, Walker (Toney, 45), Reed, Ward, Godden (Cummings, 76), Maddison. Unused substitutes: Tyler, Bassong, O’Hara, Cooper.
Bradford City: O’Donnell, Chicksen, McGowan, O’Connor, Knight-Percival, Caddis, Payne, Akpan (J O’Brien, 63), L O’Brien, Doyle (Miller, 71), Ball. Unused substitutes: Wilson, Wood, Isherwood, Devine, Wright.
Referee: S Oldham.