Button completed a move to local rivals Fulham on Tuesday.
Brentford's boss is not worried by Button's departure to QPR
Tuesday saw Button cross the west London to local rivals Fulham, signing a three-year deal after the two clubs agreed an undisclosed fee.
Button has been a key part of Brentford's first team over the last few years
Button arrived at Griffin Park in 2013 from Charlton Athletic and soon set about establishing himself as the first choice keeper at the club, making 141 appearances.
After playing a key part in helping Brentford win promotion from League One, Button has not missed a single minute of action in the Championship, helping the Bees to fifth and ninth-place finishes over the last two seasons.
David Nugent of Middlesborough in action with Button
And while Smith admits that losing a the 27-year-old is a blow, he insists that new recruit Bentley and youngster Bonham are more than capable replacements.
He told the club's official website: "I would personally like to wish David well and thank him for his contribution in both performances and attitude since myself and [assistant] Richard [O’Kelly] joined the club.
Button joins Brentford captain Bidwell in departing the club
“I have nothing but respect for the way he acquits himself to his profession and his departure will leave big gloves to fill.
“But I feel we have replacements in Daniel Bentley and Jack Bonham who are eager to fill the position that David had made his own.”
Button is the second Brentford player to join a local rival this summer, following captain Jake Bidwell's move to QPR.