QPR's Park Ji-Sung also ignored the two Chelsea players.
The game, which finished 0-0, was the first time that Ferdinand and Terry, who has recovered from his ankle injury, have met on a football pitch since the Chelsea captain's race trial in July.
Terry was found not guilty of using a racial slur against Ferdinand, after an incident in the corresponding fixture last October, but he remains the subject of a Football Association investigation over charges that he denies.
The QPR defender rejected the offer of his two rivals' outstretched hands before Saturday's game. Cole testified as a character witness for his England teammate at the trial.
It was not known how many of his Rangers teammates would follow suit but it was still a surprise to see skipper Park do the same, something the midfielder repeated during the coin toss.
QPR manager Mark Hughes said Friday that he would allow his players to make up their own mind whether to shake hands in the prematch ritual after the Premier League had declared it must go ahead.
"They had the discussion and I was made aware that some were prepared to shake the opposition's hand and some weren't," said Hughes. "I didn't know which individuals and I wasn't going to push the point. It was a personal decision for each and every one of them."
QPR fans then began making derogatory chants aimed at Terry and Cole. Fans jeered the pair every time they touched the ball as the highly charged West London derby got under way.
The enmity between Ferdinand and Terry threatened to turn the handshake, which was introduced as part of the Football Association's Respect campaign, into a farce.
Hughes wants the routine to be dropped after complaining that it "ludicrously" overshadowed the build-up to the game.
Reiterating his opposition to the ritual, he said: "For goodness sake, we've been talking about it for God knows how long. I think it's done and dusted now. It's something and nothing in my view. I thought the game was what was important today and, thankfully, it was played in good spirit. He added: "You can't get too misty eyed about the old days and how it used to be -- a lot of things have moved on for the better. But I just think this element of the Respect campaign is something that causes more problems than it solves and I don't think that was its intention when it was introduced."
Opposite number Roberto Di Matteo shrugged off the double snub and said he was pleased with how Terry -- who was cleared by a court of racially abusing Ferdinand this summer -- and his teammates conducted themselves during and after the so-called pleasantries.
"Both sets of players have shown a great attitude," he said. "They have shown how professional they are and they have played the game in the right spirit and it was a good derby to watch."
Hughes was equally effusive about Ferdinand, saying: "I thought Anton was excellent alongside Ryan Nelsen. I was pleased the players didn't lose their focus. Obviously, there was a danger of that but I realized that was not going to be the case the moment it kicked off."
It is not the first time Terry has been involved in a handshake row. Wayne Bridge snubbed the former England captain following allegations of an affair with the Manchester City defender's former partner.
And Luis Suarez refused Manchester United's Patrice Evra's offer of a handshake, despite the Liverpool forward being found guilty by the Football Association of racially abusing him earlier in the season.
Information from Press Association was used in this report.