Chelsea were denied their eighth win of the season thanks to Robin van Persie's injury-time header, which cancelled out Didier Drogba's opener at Old Trafford.
Jose Mourinho could barely hide his dismay at Phil Dowd's performance in Manchester and it appears Terry agrees with his manager.
Mourinho was unhappy that referee Dowd did not award his team a penalty in the first half when Ivanovic went down in the box during a tussle with United defender Chris Smalling during a set piece
Just in front of Ivanovic, Terry also tumbled to the ground as he battled with Marcos Rojo, but no penalty was awarded.
Van Persie's equaliser came after Ivanovic had been sent off for two bookable offences after twice fouling Angel di Maria, but Terry suggested on Instagram that it was the Chelsea right-back and himself who were sinned against, rather than sinners.
Terry wrote: ''It shows how well we are playing when you come away from Old Trafford disappointed with 1 point.
''Thanks to all the travelling fans for your great support
#JtandIVAgotdoubleheadlockedfromeverycorner.''
Dowd handed out seven yellow cards out to Chelsea, meaning the Blues will be fined £25,000.
Up until Van Persie swept home in dramatic fashion, Chelsea looked like grabbing all three points thanks to Drogba's first league goal of the season.
Many questioned the wisdom of Mourinho's decision to re-sign Drogba in the summer, but the veteran striker rolled back the years to leap high and convert a 53rd minute header to put Chelsea in front.
With Loic Remy out for a considerable time because of a groin problem, Chelsea are short of backup for Diego Costa, who has also been troubled by injury this term.
Chelsea midfielder Nemanja Matic is delighted, therefore, that 36-year-old Drogba is looking as sprightly as he did during the early stages of his career.
"Didier played very well against United, he looked like a 20-year-old out there," said Matic of Drogba, who also scored in the 6-0 win over Maribor on Wednesday.
"He was very important, kept every ball, was very strong
He was one of our most important players.
"Everybody saw that he played well
He is going to be important for us
He has already scored one in the Champions League and now another here.
"Like every player in the team, he is getting more confidence and we will see what happens in the future."
Drogba played a huge rule in helping Mourinho win five trophies during his first spell in charge at Stamford Bridge.
In total the striker scored 157 times for the west London club over eight years.
Given that he will be 37 in five months' time, it would be unrealistic to expect such a prolific goal scoring rate this season, but Matic thinks the Ivorian will be important to the squad this year for other reasons too.
"He is very important for the young players because what we're trying to do now (winning titles), he has done it first," said the 26-year-old, who also returned to Stamford Bridge earlier this year after a three-year spell at Benfica.
"He is good mentally, he talks to the young players and makes things easier for them and for me also."
Drogba is likely to be rested for Tuesday's Capital One Cup fourth round clash at Shrewsbury.
Costa, who missed the United game due to his hamstring injury, is also set to miss the game and Matic thinks it is important the Spain striker is not rushed back.
"He trained with us but I think he felt some more pain and the club didn't want to risk him," Matic said, explaining the absence of the prolific front man, who has scored nine goals in seven league games.
"Of course we need him but the most important thing is to be healthy and to be prepared for the next games
We need every player fit."
Source : PA
Source: PA