David Lloyd says England's players have been punished for the poor attitude and approach they have adopted in New Zealand.
The Sky Sports pundit was speaking as the tourists stood on the brink of series defeat at the end of day four in the decisive third Test, trailing their opponents by 391 runs with four wickets already lost going into the final day.
Bumble believes Alastair Cook's bowlers have been arrogant with the ball and pedestrian with the bat throughout the tour and says a lack of aggression or willingness to impose themselves is likely to see them lose the series to a team ranked six places below them.
"I don't like the brand of cricket that England have been playing," he told Sky Sports. "With the ball they've vanished up their own backsides and when they've come out to bat it's just a monumental block.
"Not just today, but throughout the series I haven't liked the brand of cricket. If you're looking to be number one in the world then you've got to be more forceful and look to dominate the opposition.
"The shoe has been on the other foot with New Zealand. I know that they are ranked eighth, but they're in a false position because they've got some really good batsmen, young players and an energetic bowling attack.
"Bruce Martin has been a revelation - a left-arm spinner at 32-years-of-age - and we have no clue how to play him and that's quite alarming.
"We are a far better team than we have shown and nevertheless they've got to start putting things together. We're staring at defeat here."
Bumble was stunned to see Kane Williamson take two wickets late in the day, including the prize capture of Cook, but he is more concerned by the inability of the England batsmen to cope with the swinging ball.
He also says they need to increase their scoring rate after taking just 90 runs from 313 balls on Monday.
"They didn't [reach number one in the Test rankings] by going at 1.8 or 2.0 runs per over," he added. "This boundary is 60 yards and is the flattest pitch you'll ever see but swing has got them out.
"I don't accept that. The ball does swing in international cricket, it's a Test match and these are good players. Get your cricket head on. Get your cricket brain in gear. England haven't done that."
Fellow Sky Sports commentator Michael Atherton agreed that the tourists have underperformed, but he highlighted the improved efforts of New Zealand throughout the series.
And while he was less concerned than Bumble about the pace of England's second innings, he encouraged the team to adopt a more positive approach to give themselves an outside chance of rescuing the match on Tuesday.
"I don't particularly have a problem with the tempo this afternoon," Atherton said. "It's clear what they're trying to do, but I do think you have to try and play pretty normally, even when you've got your backs against the wall.
"When you're at the crease you want to be thinking positively and your mindset wants to be about hitting the ball and scoring runs. That will help you to be positive in attack and defence, which is important.
"I would still go back to the fact that England have been outplayed here. You go back to Dunedin and England being a bit complacent and not having their game heads on there, but New Zealand have been compelling in this game and have outplayed England.
"I would put more on New Zealand having played above themselves than England having played below par."