Ince, the first black man to wear the armband for England, is the latest figure to argue against the views expressed by Campbell in a new autobiography serialised in the Sunday Times.
Campbell was capped 73 times but skippered the side only three times.
However, Ince pointed to the long list of England captains, arguing that most had to make do with relatively short stints in the job.
"There's been me, (Tony) Adams, (Stuart) Pearce, (David) Seaman, (Alan) Shearer, (John) Terry, (Rio) Ferdinand... that's a lot of big names with a lot of big egos," Ince told the Daily Mail.
"Sol's a clever, articulate man and he's a friend of mine but he wouldn't have been England captain for 10 years - nobody is.
"He has obviously had different experiences to me as a footballer and I can only really talk about my own."
Ince was made captain of England for the first time in 1993. He was initially reluctant to be known as the man to break a colour barrier, but said he later came to realise the significance of the moment.
"For me it was the pinnacle of my career when Graham Taylor made me captain, but I can remember feeling uncomfortable with the questions," he added.
"I just wanted to be the England captain, I didn't want to be remembered as the first black England captain because I didn't look at it in that way.
"Then, after the game, I began to look at it in a different way because I had a lot of parents from the ghetto sending me letters telling me it had inspired their children to get jobs or to start playing football.
"I don't know whether they were black, white or Asian or whatever, but it didn't matter. That meant a lot, to think that somehow I had inspired people I had never even met."
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ENGLAND v DENMARK
26 Sep 1948 Denmark v England D 0-0 International
02 Oct 1955 Denmark v England W 1-5 International
05 Dec 1956 England v Denmark W 5-2 FIFA World Cup
15 May 1957 Denmark v England W 1-4 FIFA World Cup
03 Jul 1966 Denmark v England W 0-2 International
20 Sep 1978 Denmark v England W 3-4 European Championship
12 Sep 1979 England v Denmark W 1-0 European Championship
22 Sep 1982 Denmark v England D 2-2 European Championship
21 Sep 1983 England v Denmark L 0-1 European Championship
14 Sep 1988 England v Denmark W 1-0 International
07 Jun 1989 Denmark v England D 1-1 International
15 May 1990 England v Denmark W 1-0 International
11 Jun 1992 Denmark v England D 0-0 European Championship
09 Mar 1994 England v Denmark W 1-0 International
15 Jun 2002 Denmark v England W 0-3 FIFA World Cup
16 Nov 2003 England v Denmark L 2-3 International
17 Aug 2005 Denmark v England L 4-1 International
09 Feb 2011 Denmark v England W 1-2 International
Five England players missed training on Monday morning as Roy Hodgson began preparations for Wednesday's friendly against Denmark.
Kyle Walker, Andros Townsend, Adam Lallana, Steven Caulker and John Ruddy all missed the session at Tottenham's training ground.
All five are undergoing recovery work inside the state of the art facility near Enfield. Townsend, Caulker and Ruddy all played on Sunday so they were always likely to miss Monday's session.
Walker reported with his team-mates to the training ground but he was walking gingerly due to a hip injury.
Spurs boss Tim Sherwood said following the 1-0 win over Cardiff that the right-back would not play against the Danes.
Lallana played the whole of Southampton's 3-0 defeat to Liverpool on Saturday but was not deemed fit enough to train with his England team-mates on Monday.
Lallana's team-mate Luke Shaw took part in his first England training session. The 18-year-old could make his international debut at Wembley on Wednesday.