Allardyce fought a rear-guard action to keep the side up last term after inheriting a team second from bottom of the Premier League last December.
Roberts believes the former Bolton and Newcastle manager will now do good business in the transfer window to put Rovers in a strong position next term.
He told the Daily Star Sunday: "The manager has worked hard to turn around our fortunes.
More praise"He deserves a lot more praise than he has received for the wonderful job he's done.
"There will be players moving out in the summer so we have to see what happens there.
"But we trust Sam to bring in the right replacements and he won't rest until he does.
"I've been at clubs where staying up is good enough but that isn't acceptable under Sam and I'm sure he'll bring in the players to put us in a strong position next year."