Grant was singled out by the Chelsea boo-boys after taking Cole off in the second half of their 2-1 Premier League victory over Newcastle.
The Israeli coach was taunted with chants of 'You don't know what you're doing', but Cole shrugged off the criticism by focusing on their results over the holiday programme.
Cole declared: "Fans have always got their opinions. What's important is the result. The main thing is we get the results. We won that game. We keep on winning.
"We took 10 points out of 12 over Christmas in a difficult period, with a lot of injuries.
"If you took those players out of some of the other sides, they would struggle to win as we have.
"Everyone has got a different opinion. All that's important is that we're all pulling in the right direction, pulling together and hoping to achieve things.
"Any club that's winning games is a nice place to be. We're happy, but there are still improvements we have to make.
"We had a turbulent time at the start of the season. Avram came in and steadied the ship. He has changed it slowly.
"We're still in touch with the leaders, in all the competitions, and the lads have taken to him.
"We're improving every day. We're trying to employ the new tactics and style the new manager wants. It's change.
"It's about learning and adapting. We're winning games while we're in transition. A lot of clubs go years without winning trophies while this sort of thing happens, but we're winning games, we're a happy camp and we're pulling together."