The promotion of Trollope, 43, was confirmed on Wednesday with Dalman promising him full control of the first team and funds to bolster his squad.
Trollope worked as Slade's assistant from February 2015 and has been told the Bluebirds hierarchy expect a top six finish.
"It is not us taking the cheap option," Dalman told BBC Radio Wales Sport.
"It could turn out to be a very expensive option."
Slade has taken up a new role as head of football, in which he will oversee scouting, among other duties.
Trollope will not report to Slade, and has already started to change his backroom staff with coach Scott Young being moved from first team duties.
Dalman believes Trollope's appointment underlines Cardiff's commitment to stability and has explained the club will allow the former Bristol Rovers manager to be his own man.
"We have [had] stability over the last 18 months. The team is not far off, let's be honest about that," he said.
"Paul is absolutely able to bring in his own coaching team, it is entirely up to him how he builds that and I will support him with club resources."
Dalman entirely dismissed the notion the club missed a trick by appointing from within.
"First of all, we interviewed candidates from outside of the club as well, and some very, very good candidates actually. I was genuinely very surprised and impressed by the number of people who have shown interest," he said.
"We felt that when you look at the history of the club and the disruptions and difficulties that we have had, we felt continuity was important.
"And the resources we are about to have we want to put into the squad, rather than anywhere else. There will be money available for Paul, absolutely."
Trollope has been told clearly he is expected to finish in the top six next season after the Bluebirds finished this campaign eighth in the Championship.
"We need to get promoted and we will do the best that we can," Dalman said.
"It is challenging, especially with the teams coming down - Aston Villa, Norwich City and Newcastle United, these are not the sort of teams you take lightly.
"I think Paul has a real task ahead of him, but you've got to expect us to be at least in the top six, if not in the top four, if we make the investments we are planning to make."
Trollope will not be reporting to Slade as he takes control of all aspects of the first team at Cardiff City Stadium.
"Russell has now gone to head our football side; he will be helping us with all football matters, apart from the first team," said Dalman.
"Paul Trollope will report directly to our CEO Ken Choo and very much has a free hand.
"And that is the big significant change, that we are allowing Paul to express himself on the pitch. I think he will do a good job for us."
Chairman Mehmet Dalman says Paul Trollope is not a "cheap option" to succeed Russell Slade as Cardiff boss.