Mourinho came up with that tag after his side snatched a controversial 2-2 draw at home to the Baggies a fortnight ago - thanks to a dodgy, last-gasp penalty.
Northern Ireland star Brunt, 29, said: "The so-called Mickey Mouse club were winning at Chelsea with two minutes to go.
"No, we're definitely not a Mickey Mouse club.
"We are more respected now and we're a match for anyone.
"These games and results show how much we have come on over the last few years. It speaks volumes.
"We have had a fortnight to brood about the penalty.
"We were devastated not to get our first win at Chelsea in 35 years and to have it taken away by that decision was very disappointing.
"The powers that be felt they had to apologise to us - and at the time all the players knew it wasn't a penalty.
"But Chelsea have a great record there under their manager and they were within a whisker of losing that.
"People say things in the heat of the moment and regret it later.
"I'm sure there was a bit of that but it's done and dusted now.
"If we'd been offered a point at the Bridge beforehand, we would have taken it. Then again, we should be sitting here with two more points in the league."
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