Graeme Smith criticises Alastair Cook's 'stale' captaincy and England's decision to drop Kevin Pietersen

Alastair Cook needs to "answer important questions in his role" as England captain, according to Graeme Smith. The former South African captain labelled Cook's beleaguered side "stale", suggested England have made a mistake in jettisoning Kevin Pietersen and, just for good measure, questioned whether Stuart Broad shirked the responsibility of leadership during the World Twenty20, the final ignominious chapter in England's disastrous winter.

Smith did for three England captains during his long tenure in charge of South Africa – Nasser Hussain, Michael Vaughan and Andrew Strauss – and has now passed an unimpressed judgement on the two incumbents, as well as questioning how England's management have handled Pietersen.

"[Cook] needs to answer some important questions in his role," said Smith, speaking at The Oval, where he will captain Surrey – and Pietersen – this season. "Do the players trust him? It's going to take a lot of energy [to rebuild after the winter]. Captaining and opening the batting is a really taxing job. He's also going to have to focus on performing, scoring runs – if he scores runs it will really help his captaincy.

"He knows the environment, he knows the direction he wants to take the players with whoever the new coach is going to be. Once he makes those decisions then he has to really back it and go for it."

Smith, who retired from international cricket following South Africa's defeat by Australia last month, said that he had initially been taken by surprise by England's rapid demise Down Under but, with the rot now set in, the need for change was pressing.

"To me, England look a little bit stale, they need new energy, they need a direction, someone to galvanise them," he said.

Smith has had several conversations with Pietersen, although no in-depth discussion yet as to what went on over the winter. Smith believes Pietersen remains a "match-winner" who should have been better handled by England's management.

"In any environment there are a lot of different personalities, so you need to be able to manage. That's part of being able to be a leader. I was initially very surprised [about Pietersen's axing]. I would have thought the environment could have managed him – a match-winner like that, if he's performing well and you get him motivated. You can't but help looking at the Twenty20 World Cup and feel he would have added value.

"I'm speaking from an outsider's perspective, but it is surprising if you have a really quality player like that who is not at the back end of his career – he is kind of in the middle of his career [and] still has a few good years left in him – that you would not have tried to make it work. If it was a guy in his last season and he is becoming grumpy then you start to look at things differently. But Kevin's fit, he's healthy, he's still performing well. It was surprising.

"It's always nice to have a player who can win you games single-handedly, it's nice to build teams around players like that. Players like that can win you a competition.

"International cricketers spend a lot of time on the road, a lot of time with each other and a lot of time in pressurised environments where they need to perform, so you can't expect to be rosy all the time."

During England's embarrassing defeat by the Netherlands at the World Twenty20 earlier this week, Smith, watching on TV, tweeted: "Could be mistaken but never saw Broad bowl in power play or death overs! Protecting himself?"

Asked to elaborate on that view, he said: "It was an observation: a high-class, experienced bowler not bowling in the toughest part of the game. I think there was a trend also in a couple of games. The challenge as a captain is you need to front up. You ask a lot of your players. You put them in pressure situations and you also need to take responsibility for that. I would be surprised if there weren't a couple of players saying, 'Why doesn't he bowl in those circumstances?' That's an important part of leadership, leading by example. I think he has the ability to lead by example so I was surprised."

On another of the casualties from England's winter, Jonathan Trott, Smith was more circumspect as he outlined the obstacles that lie in Trott's path following his "burnout" in Australia.

"Everywhere he goes, every interview he does, every crowd he plays in front of, every team he plays against is going to bring that up, so how he copes with that is the only important thing," he said. "In international sport nobody holds back so it will fall to him as an individual how he can handle that."