There has been bad blood between Hughes' Fulham side and the Potters all season, stemming from a reckless tackle from Andy Wilkinson on Cottagers striker Mousa Dembele in a Carling Cup clash in September.
An enraged Hughes snubbed Pulis' handshake at the end of the game, and Pulis then blanked his opposite number after Fulham's 2-0 win at the Britannia over Christmas.
But Hughes said: "I'll always offer my hand, it was blown out of proportion.
"It was just tit for tat. I did a similar thing to Tony because I was a little bit upset with a challenge on one of my players in the League Cup tie.
"It just happened, I was probably a little bit emotional about it and probably showed it in the wrong way and Tony maybe showed his displeasure at being beaten at home in the wrong way. So we need to grow up, probably."
When asked if he thought his handshake would be accepted when the sides meet at Craven Cottage, Hughes added: "Let's hope so. We're two Welshmen, there's no reason why it shouldn't be."
Seven points from their last four games has edged Fulham away from the Barclays Premier League drop zone after a slow start to the campaign.
And Hughes now has his sights set on a strong second half to the season and a top-10 finish in a congested division.
"We are playing okay," he added. "We've been playing fine for the majority of the season but we struggled to convert draws into wins and that put us under a bit of pressure.
"But in terms of our general peformances in recent weeks I've been really pleased with what we have produced."
Hughes wants to add Chelsea youngster Gael Kakuta to his squad but the Blues have yet to decide whether to let the 19-year-old go out on loan.
"He's a player I know and I like the qualities he has," said Hughes, who has also been linked with Robbie Keane, Shaun Wright-Phillips and Henri Lansbury.
"We are having lots of conversations about lots of players, but at the moment we don't know if any will go through.
"There is a lot of interest out there, whether we can conclude the deals only time will tell."
New Stoke signing John Carew is keen to seize his chance after joining on loan until the end of the season.
The 31-year-old is out of contract in the summer and believes a successful four months at the Britannia Stadium could lead to a permanent deal.
"If I'm happy and the club is happy, if I enjoy it and it goes well enough, then we can decide that in the summer," Carew said.
"The important thing now is to make the most of this opportunity.
"I'm looking forward to the challenge and I am happy to be here.
"Although I had other offers, I saw Stoke as the best team and the strongest team, so this is a great chance for me to join a side fighting in the top half of the table.
"Tony Pulis has shown great confidence in getting me here so I want to repay that faith.
"He's a great manager who created a big impression with me, so I am delighted I have been given this opportunity to work with him."
Stoke's assistant manager Dave Kemp hopes they will be able to benefit from Carew's desire to prove a point to Villa boss Gerard Houllier.
The Norway international effectively ended his three-and-a-half-year career at Villa Park with his loan move.
His relationship with Houllier - who has got rid of Carew for the second time in his career having offloaded him to Villa as Lyon boss in 2007 - has been strained in recent months.
The striker called Houllier "disrespectful" after he was challenged to earn a new contract, with the Frenchman responding by calling the former Valencia forward "stupid" and telling him to stop "living in the past".
"You hope with an experienced player you get someone with a point to prove," said Kemp.
"The fact he has not been that involved so much this year (means) he might come here with something to prove, that maybe he was left out of the equation (at Villa) too early.
"He is a proven Premier League striker. For a big man he has got good feet and skills and can bring people into the game and is good in the air and he scores goals - what is there not to like?"