Ramsey, Les Ferdinand and Kevin Bond will lead the team into Saturday's Premier League match against Southampton after Redknapp quit on Tuesday due to knee problems.
Former Tottenham Hotspur manager Tim Sherwood was immediately linked with the job but media reports said negotiations with him had stalled.
"It's always a surprise when something like this happens," Ramsey, the manager of QPR's Academy programme, told a news conference on Friday. "It was a shock, a big surprise.
"We all knew Harry had a knee problem, but he never moaned. He just got on with the job. I'm in this role with Kevin Bond to steady the ship until the club appoints someone to take the role.
"It's down to the owners to decide who they think is the best fit for the club. They will decide who is the best for QPR.
"It's a proud moment for me. We've got a great set of fans and we want to repay their loyalty tomorrow."
QPR, who are 19th in the table and facing an immediate return to the Championship (second tier), go into the Southampton match after losing their 11th successive away league game last week at Stoke City.
Southampton, who beat QPR 2-1 at home in September, are having their best season since the 1980s and lie fourth, chasing a Champions League spot.
"Southampton have been outstanding in the Premier League," Ramsey said. "They've been a breath of fresh air for the division.
"We need to be on the front foot, giving maximum energy and showing some flair. We need to get fans off their seats. The players really need to step up now and achieve what they're capable of.
"All I am interested in is getting three points tomorrow. Whoever is fit and available will be in contention."
(Reporting by Mike Collett, editing by Ed Osmond)
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