Republicans shouldn't let the fact that they won the White House, as well as Congress, cover up the real challenges ahead, and should not concentrate effort on prosecuting former Secretary of State Hillary Clinton, Rep. Tom Cole said Monday.

"Looking at the past is a big mistake," the Oklahoma Republican and deputy whip told MSNBC's "Morning Joe" program. "Trying to settle scores is always a waste of time in politics. We need to look at what the president-elect's program is and start moving that through Congress.

"That's the way I think we can make strides. If we're persecuting people that lost the last election, we're making a mistake of a lifetime."

If the race had engaged more millennials and minorities, Cole continued, Republicans "would not have won."

"We have an opportunity to move forward here and reach into communities we haven't done well in," said Cole. "[Donald] Trump himself did some of that during the course of the campaign."

Cole said he believes Trump has been "pitch-perfect" since election night, and he'll be the person who sets the tone for his administration.

The Oklahoma lawmaker also praised Trump for choosing Republican National Committee Chairman Reince Priebus as his chief of staff.

"He's somebody that's well known and trusted," said Cole. "He managed to win confidence of everybody on the side of the great divide in Republican politics, and led us to a victory that a lot of people didn't see coming."

He also praised President Barack Obama and Clinton for their tone as well, but said he wishes protesters against Trump's election "would just take a cue from their leaders, who have acted responsibly and in the best traditions of the country."