Experienced shot-stopper Button, 33, came under more heavy fire from Baggies fans after his error led to the Welsh visitors' early opener during Saturday's 3-2 home defeat at The Hawthorns.
It was the afternoon many home fans sounded their frustration at boss Bruce and Button's position as the club's No.1 has also come into question.
Button and Albion have managed just a single clean sheet from 11 league games so far this term. The keeper has been blamed by fans for not making enough saves but under-pressure boss Bruce wants to see him better protected.
"He's frustrated because at the end of the day goalkeepers don't want goals to go in, they pride themselves on keeping a clean sheet," said the Albion boss.
"We have to help him more, he hasn't helped himself today, of course, but we haven't helped him enough.
"If we have to keep scoring two or three – which we seen to do by the way – then we're not going to win football matches.
"So we have to do the basics better, I'll have a big, long look at how we can make that better."
Former Fulham and Brentford man Button started the contest against Swansea with a wonderful flying save to deny Matthew Sorinola but was then found wanting as he failed to grasp the resulting corner, allowing Sorinola to score.
He could do nothing about follow-up goals from Olivier Ntcham and Michael Obefemi's last-gasp winner as Albion lost 3-2 at The Hawthorns for the second game in succession.
Bruce takes his lowly Baggies side to 14th-placed Preston North End, who are without a win in four, tomorrow.
The manager, meanwhile, would not answer whether Button would remain as his first choice between the sticks, with Alex Palmer unused in reserve and fellow academy product Josh Griffiths on loan at Portsmouth in League One, where there is a recall option.
Bruce said: "I don't think that's a question I should be answering today."