Injury and illness have meant Olsson has played just one match - the FA Cup victory at Blyth - for the new manager but he has seen enough on the training ground to know he is the man to save Rovers, currently 18th in the Premier League.
"He (Ince) tried his best but when he was here we were low on confidence," said Olsson.
"Since Sam came in we have been working hard in training and we know we can get out of the bottom three, it will just take a bit of time.
"We work as a team, not individuals. There is more communication and that helps a lot on the pitch.
"Sam has been in the Premier League for a long time compared to Paul Ince. Ince needed to learn more because he was new to the game.
"Sam knows what he is doing and that is why I'm not bothered if I'm not playing because I'll just learn what others are doing on the pitch.
"I think our confidence has gone much higher than when Ince was here."
Olsson is likely to get a run-out in the FA Cup fifth-round replay at Coventry on Tuesday - as are a number of the fringe players - and is confident they can book a home clash with Chelsea in the quarter-finals.
"I've been out with injury and viruses but if I get my chance I'll do my best," he added.
"I saw a bit if the last game [against Coventry] and in the second half they were good.
"We have to be focused and start playing how we do and I think we will be fine.
"We are playing good football when we are playing together. We know we are good as a team and we know we can beat Coventry even if we don't have the strongest squad.
"If he (Allardyce) plays the young ones or the ones who don't play every week, then the others can think about the Premier League games.
"It is an important game because we want to go to Wembley but the Premier League is more important and we have to focus on that."
Allardyce said the chance to play Chelsea at home in the next round provided an extra bonus for getting through against the Sky Blues.
"A victory against Coventry would take us into the Chelsea game and mean we would be one win away from at least playing once at Wembley because that semi-finals are there," he said.
"That is a great incentive and we have fought long and hard to get where we are at the moment."
, Coventry 15/8
, Draw 12/5