Wallace missed a short birdie putt on the 17th hole in the final round and reacted angrily after failing to convert a longer attempt on the 18th which could have given him the title.
A visibly upset Wallace then looked on as playing partner Marcus Kinhult holed his own birdie putt to claim his first European Tour title at Hillside.
“The way I reacted in banging my putter on the green on 18 was not right and, for that, I can only apologise,” said Wallace.
“I’m really disappointed in the way I behaved.
“For 71 holes I’d done really well, then let myself down badly with one petulant act. The best players in the world don’t do that so why should I?
“That’s not who I am and, in that moment, it was just pure passion to win.
“I’m not, though, disappointed with the way I played. I hit 82 per cent greens in regulation, my best ever, so it feels like a step in the right direction compared to a few weeks ago.”
Wallace’s share of second place with defending champion Eddie Pepperell and Scotland’s Robert MacIntyre at least lifted him to a career-high of 31st in the world rankings ahead of this week’s US PGA Championship at Bethpage.
“I’m excited about what I’m doing, but genuinely there’s no expectations for this week at the second major of the season apart from trying to control the emotional side of things,” added the 29-year-old Londoner, who had a hole-in-one on his way to a tie for 19th in last year’s US PGA at Bellerive.
“I’ve never played Bethpage but it looks brutal and the weather does not look great, so it’ll be cold and playing long. For me, it’s the next step in going from 31st in the world to the top 10.”
Tournament organisers, meanwhile, have described the return to Bethpage of the event for the first time since 1949 as “hitting the lottery” as it welcomes newly-crowned Masters champion Tiger Woods and his rivals.
This is the first year the tournament has moved from its traditional August date to May.
“We were very excited about the May change even before Tiger set off his fireworks in Georgia,” Seth Waugh, the PGA of America chief executive, said.
“We think we made a great decision but we’d rather be lucky than good as well.
“We thought it was smart; it looks brilliant now.”