De Gea was widely criticised following Tottenham's stoppage-time equaliser a fortnight ago, and was under further scrutiny on Wednesday following Southampton's early goal at Old Trafford.
The former Atletico Madrid goalkeeper produced a number of impressive saves at Fulham on Saturday that led to a crucial 1-0 victory, and Rooney praised the Spaniard despite recent criticism.
"David has made some great saves over the last few weeks," Rooney said.
"I know he got a little bit of criticism after the Tottenham game but it wasn't the biggest mistake I've ever seen.
"We're all behind him. He's a great player for the future as well."
United defender Jonny Evans added: "People underestimate the reflexes he's got.
"We are used to seeing him do that. His shot-stopping ability is very good and his save from (John Arne) Riise was excellent."