The 45-year-old has endured something of a rollercoaster ride since being appointed to his first senior role when taking over from Andre-Villas Boas in December.
Sherwood, appointed on an 18-month deal by Spurs chairman Daniel Levy, publicly criticised his players after the 4-0 thrashing at Chelsea, and was then involved in a touchline row with Benfica boss Jorge Jesus, whom he blasted as "classless" following the 3-1 home defeat in the Europa League on Thursday night.
Wenger, who is closing in on his 1,000th match in charge of Arsenal, believes every manager needs time - even if things do not always go to plan.
"I am always pleading for stability. Maybe you could say I'm pleading for myself. I always think technical stability is important," said Wenger, who has seen 10 Spurs full-time managers come and go since his appointment in late September 1996.
"But it will become more and more difficult because in every single game there is a trial happening now on what has the manager done right and wrong. The stability will certainly be much more difficult."
Wenger added: "I don't know Sherwood as a coach. I knew him as a player because I am a long time in this job.
"I like the fact that he has learned his job and gets his chance.
"In England you rightly complain that young managers don't get a chance. When you get one you have to support him."
Arsenal saw their own European ambitions ended despite a 1-1 draw away to Bayern Munich on Wednesday night, as they went out 3-1 to the Bundesliga leaders on aggregate in their Champions League last-16 clash.
The Gunners will be out to kickstart their Barclays Premier League title ambitions with a first league victory at White Hart Lane since 2007, where defeat for the hosts could all but end their chances of breaking into the top four.
"Everybody at the club is focused for this game and for the end of the season to make a period where you turn your season," said Wenger, whose side recovered from defeat at their north London rivals this time last season to embark on a winning run to snatch fourth place.
"We have the strength. There are moments in a game and there moments in a season where you have to be there.
"With the season that we have in front of us now everyone game is a final for us.
"We are in a position where we can do well in the league, where we can do well in the FA Cup and that demands confidence and confidence is linked with results."