Ipswich are currently four points adrift at the bottom of the Championship - a run of form that has seen manager Paul Jewell sacked.
And Wellens, who has been at the club less than a month since signing on a short-term deal from Leicester, feels more changes are required if they are to escape the drop.
"A new manager needs to come in and put a rocket under their backsides because there are not enough people who show they care about losing a game of football or even their own careers," said the 32-year-old, quoted in the Daily Express.
"One of the coaches said that the old manager got stick for bringing in loan players, but it is the loan players who are showing they care and that is a sad indication of what is wrong.
"We need people to show passion, to show they care. It is difficult when you are getting the ball and no one else wants it. It is human nature when you are under pressure to go and hide but we need a better attitude, and to act like men.
"I have always thought of Ipswich as a nice club and that was confirmed when I got here. It is a little too easy, too cosy.
"I can't see Ipswich ever winning a game unless they are at their best and everything is going for them. To be a strong club in the Championship you have to win when things are not going well.
"I can fully understand why the club have been done by five and six goals this season."