Wilshere made his first start for the Gunners in 493 days and was their best player as Theo Walcott scored the only goal in a dominant 1-0 win for the the Premier League side.
Doncaster held their own for much of the contest and hit the bar late on but were largely on the back-foot, with Wilshere often pulling the strings.
Following a string of injury problems and a loan spell at Bournemouth, this was Wilshere's first time in Wenger's starting line-up for 16 months and the Frenchman was suitably impressed.
"I wanted to leave him on to give him 90 minutes and overall I think it was an ideal game for him tonight to gain confidence and fitness," he said.
"We'll see after that how he will respond, normally he's alright after the game.
"I think you have to put this game into perspective as well - it has not exactly the intensity of a Premier League game, but it's important for him to build him up gradually."
Arsenal captain Per Mertesacker was also pleased to see Wilshere back and praised the bravery of the England international.
"It was very good to have him back out there," he said.
"You can see that he's getting more comfortable with his position now
He's brave now and he trusts his body
That's the most important thing, that he's capable of playing 90 minutes."
Darren Ferguson led Doncaster into the game on the back of just one win in Sky Bet League One so far this season.
But, after seeing his side hang on against Arsenal's early assault before pushing for a dramatic equaliser late on, the former Peterborough boss was pleased with their efforts.
"I'm proud of the players," he said.
"In a cup match you need a bit of luck but it was a fantastic learning curve in terms of concentration for my players.
"When you are a lower league team playing a team from the top level the opening 20 minutes can be difficult and I felt we were getting through that when Walcott scored.
Ferguson's father, former Manchester United boss Sir Alex Ferguson, watched on from the stands as part of a record-low Emirates Stadium attendance.
Wenger revealed he had invited his former rival along to watch the contest.
"I invited him tonight," he said.
"Sport is very good in that you fight against each other and with respect
He was a big personality in the Premier League."
Arsenal will host Norwich in round four as Wenger seeks to win the competition for the first time.
Source : PA
Source: PA