It comes as the party's UK executive met to set the timetable to choose Ed Miliband's successor.
Cardiff South and Penarth MP Stephen Doughty said voters in Wales and England had a "lot more in common" than "perhaps many would care to admit".
He said the new party leader should be chosen from MPs first elected in 2010.
That would include shadow business secretary Chuka Umunna and shadow care minister Liz Kendall, who have already said they will stand, but rule out potential leadership contenders Yvette Cooper, the shadow home secretary, and Andy Burnham, who speaks for Labour on health.
Further high-profile party figures are expected to join the contest.
Mr Doughty told BBC Wales: "I think we need a fresh set of faces, not just in the leadership and deputy leadership, but also in the leadership team in the shadow cabinet and at the top of the party."
He said the idea of what he called "Welsh exceptionalism" within his party was wrong and "has to be put to bed once and for all".
"Many people in Wales wouldn't like it, but there is a lot more in common with voters in Wales and England than perhaps many would care to admit, and I think we need to be honest about that," Mr Doughty added.
Labour lost Gower and the Vale of Clwyd to the Conservatives in the general election, and failed to take target seats including Cardiff North and the Vale of Glamorgan.
Labour won 25 out of 40 seats in Wales, but had expected to improve on the 26 seats it won in 2010, while the Conservatives won 11, their best performance in 32 years.
Labour needs a break with the past and an honest assessment of why so many Welsh voters chose the Conservatives over them, one of its MPs has said.