Clarke's men have won just one of their last 15 matches - a 2-0 friendly victory over Gibraltar in June - and have failed to win a competitive game for more than a year.
Scotland have been partly victim of their earlier success under Clarke as that run includes their participation at Euro 2024 and in the top tier of the Nations League after securing promotion in 2023.
Scotland face a daunting task to avoid losing five competitive matches in a row for the first time in their history when Portugal visit Hampden on Tuesday.
Clarke said his squad deserved time to turn things around after ending a 23-year wait to reach a major tournament by qualifying for the last two Euros.
"After 20 years in the international wilderness, this group of players have been to two major tournaments," said Clarke at his pre-match press conference on Monday.
"They've got promotion to this top level of the Nations League, so I don't understand why people would be doubting about this group of players.
"It's a tough moment, there's no doubt about it, but we believe in ourselves."
Clarke has also had to cope with a lengthy injury list since Euro 2024, but there have been promising signs in narrow defeats to Poland, Portugal and Croatia in Scotland's last three outings.
"They understand that we're playing difficult opponents. They understand also that the squad could be stronger, everyone knows that. All these things are there to be seen," added Clarke on maintaining the support of the Tartan Army.
"We know we have to be very good at everything we do in the game. Hopefully we can get the result that might just change the whole mood about the place."
The emergence of teenager Ben Doak is cause for optimism for Scotland fans.
The Liverpool winger, who is on loan at Middlesbrough, impressed on his first international start in Saturday's 2-1 defeat away to Croatia.
"We know Ben is a talent. We want him here for the next 15 years, not the next 15 months," said Clarke.
"We've got to get the balance right between giving Ben the opportunity to play, because he's more than capable, but also making sure we protect him a little bit and don't overhype him."