The tourists slipped to a nine-wicket defeat at the Oval on Monday as England wrapped up a come-from-behind 2-1 victory in the three-match series.
Shortly after the loss it was announced that Boucher would step down as head coach after the T20 World Cup that gets underway in Australia next month.
Speaking immediately after the defeat at the Oval - but before he addressed his players about his resignation - Boucher lamented his team's batting woes in what was to be his final Test series in charge.
"I'm disappointed because I think it's a missed opportunity," he told reporters.
"We played some very good cricket, but then we just didn't put the runs on the board, so we never quite knew how much we could've tested England.
"We believed we had the bowlers to be able to take 20 wickets, but the bottom line is you've got to score runs and we never got them on board."
The Proteas only scored one half-century across the three Tests - opener Sarel Erwee's 73 in the first Test at Lord's - while the hosts had four half-centurions in the series.
Ben Stokes and Ben Foakes also struck hundreds for the home team in the second Test in Manchester and the currency of runs ultimately proved the difference between the sides.
Boucher added: "We tried really hard, I can see it, the guys are trying really hard, but they fell short with regards to their batting technically.
"We knew (beforehand) that England had good bowling, we knew we would be tested, unfortunately we just could not stand up to it.
"We always knew we were going to be under pressure if the conditions went around a bit. In South Africa the conditions are different, the ball doesn't swing, our contact points are a little bit different."
South Africa still sit second in the World Test Championship (WTC) table and will have to fix their batting problems ahead of the next Test series away to Australia at the end of this year.
It won't be Boucher's responsibility to do so any longer though as Cricket South Africa (CSA) begin their search for a new head coach.