At Edgbaston on Saturday, England will seek to make it three wins out of three in Group B, hosting Australia, who need to win having had two games washed out.
Roy has made only 27 runs in his last five innings for England but Morgan told BBC Sport: "We believe in him.
"He has been a huge part of our team and we are a very strong side when Jason Roy is firing."
South Africa-born Surrey batsman Roy, 26, made his one-day international debut in May 2015 and has played in 45 matches, scoring 1,458 runs at an average of 34.
He made two hundreds in three matches against Sri Lanka last year - his highest ODI score of 162 taking only 118 balls - but having made three successive half-centuries in India in January, he has reached 50 only once in his last 10 innings.
Morgan, one of four England batsmen to pass 50 in the tournament thus far, said he would not be telling Roy to curb his naturally attacking instincts at Edgbaston.
"I don't think anyone uses the phrase 'knuckle down' in white ball cricket anymore, I definitely won't be telling Jason Roy to knuckle down," he told BBC cricket correspondent Jonathan Agnew.
"Everybody is in a bit of nick and the fact that one guy isn't and we're still winning games says a lot about this team."
England, twice beaten finalists in the competition, most recently against India in a rain-reduced match at Edgbaston four years ago, have won 10 of their last 11 one-day internationals, their only defeat coming in a dead rubber with South Africa at Lord's last month.
"Everybody seems to be firing, it's the type of performances you need for guys to rub off on each other because even if you're in form sometimes you won't come off but you know someone else has your back in the group," Morgan said.
Having already secured qualification for the semi-finals, the skipper spoke of a potential 100% record in the group stages: "It'd be a huge confidence-booster. If we're trying to win global tournaments we need to beat sides like Australia. It's a great challenge and one we're really looking forward to."
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Australia have won the tournament twice in addition to four of the last five World Cups and skipper Steve Smith says Saturday's match is a must-win encounter for his side.
"That usually does bring out the best of the Australian team in big tournaments, but England have improved and we're certainly going to have to be at our best to beat them," he said.
The Australia batsmen have faced only 25 overs in the first two matches, both curtailed by rain, and Smith said: "It's not ideal we haven't got through a full fixture yet but we can't control the weather. For us it's just about treating it as a quarter-final and playing the way we know we are capable of."
Asked about the pay dispute with Cricket Australia that continues at home, Smith added: "The players have been really united, there hasn't been much talk about it as a team.
"I said at the start that an ICC tournament only comes around every four years. It's the second biggest tournament after the World Cup so you've got to be switched on for every game."
England captain Eoin Morgan says "runs are just round the corner" for opener Jason Roy in the Champions Trophy.