Speaking to Times Radio on Monday, Eustice said that the resignation of Dowden, the co-chair of the Tory party, “was a surprise and I was certainly disappointed”.
“I really regret that he decided to go, I think he knew the party and CCHQ quite well.
“But I can understand the frustrations that he felt.”
In his resignation letter, Dowden said that someone “must take responsibility” for the poor by-election results, in what has been perceived as a dig at the prime minister.
But Eustice claimed that he didn’t think Dowden “needed to do that”.
He said the government has had a difficult six months, but “I don’t think he needed to take responsibility in the way he chose to”.
He also admitted the by-election results – which saw the Tories lose one seat to Labour and another to the Lib Dems – were “incredibly disappointing”, but again highlighted that the government planned to get things back on track ahead of the next general election.
Pressed on the tensions within the Conservatives at the moment, Eustice claimed that the party had put the confidence vote – where 148 MPs voted for Johnson to leave office – “behind them” for now, even though it was a “big concern”.
He also tried to emphasise that the government remains united despite the shock of Dowden’s departure.
“The rest of cabinet are working with [Boris Johnson] on [the task in hand], we stick together through difficult times as well as good times.
“We’ve had some challenges lately, and we’re going to keep working on those really big issues,” he told BBC Breakfast.
The environment secretary was also pressed over Johnson’s recent claim that he planned to stay in office until the 2030s – only for Downing Street to allege he was joking.
“Prime ministers can’t really win in this situation,” the cabinet minister said.
Eustice said: “What the prime minister was really saying was he’s got no plans of going, he’s got a lot to deal with at the moment.
“We’ve got a very precarious international situation and he’s playing his part there, even this week.
“We’ve got challenges coming out of the pandemic with inflationary pressures on the pandemic, without navel-gazing about who should be leader of the party and so forth.”
He said the government had “a lot to deal with”, and that in a year, “people might see things differently” once some of these issues have been addressed.