Newcastle were booed off after their 2-1 home defeat in the Tyne-Wear derby on Sunday, with the Magpies now trailing Sunderland in the Premier League table after losing to their nearest rivals twice this season.
Newcastle have badly unperformed in the league and now face an uphill battle to qualify for any European competition next term.
There's increasing discontent among supporters and growing pressure on Howe from the stands.
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But Rooney believes Howe's position as head coach should be secure, and has told fans "not to let their emotions get the better of them".
Speaking on the Wayne Rooney Show, the former England striker said: "I'd just say to Newcastle fans, be careful what you wish for.
"I've heard a few times now the booing and people questioning Eddie Howe. Eddie Howe is one of the best managers in the Premier League, no doubts.
"Don't push him out, don't force, keep pushing and forcing him, because you let emotions take over and you lose games.
"I know they haven't been great in the league this season, they've had injuries and they've struggled to replace Isak and his goals from last season, but just be careful what you wish for because honestly, there's no doubt he's a top manager."
Newcastle have paid the price for their nightmare summer. Operating without a sporting director, the Magpies failed in their bid to keep wantaway Alexander Isak and missed out on a number of targets, before landing Nick Woltemade and Yoane Wissa.
Woltemade made a bright start to life on Tyneside but has been shifted to midfield of late, while Wissa has endured a nightmare first year in the North East.
Rooney said: "They look like panic buys because I think they went for Sesko and Mbeumo.
"It looks like they had to bring players in and the ones they've brought in haven't performed well. It's a lot of money and a lot of goals taken out from last season.
"He's playing Anthony Gordon up front, so you're missing him on he left where he's dangerous.
"I know Harvey Barnes has done really well but he seems to be putting players in different positions because he has to rather than because he wants to.
"He's a top manager and I just hope Newcastle fans don't let their emotions get the better of them and put the board in a position to make a decision because he'll be very difficult to replace."
Emotions on Wearside are very different. Sunderland have enjoyed a glorious first campaign back in the Premier League and are just three points behind seventh placed Brentford with seven games to play.
Rooney said: "To win both derbies is massive. The Newcastle fans pride themselves on those games as well and to lose those games is hard.
"Sunderland, to come up and win both derbies, to be in the position they are, they've had an unbelievable season."