The League Two top-of-the-table clash was full of good passing football, but neither team found a cutting edge.
Kitson was dismissed in stoppage time for a second yellow card, having been booked for a foul in the first half.
It was Wilder's 250th game in charge of Oxford and he reflected afterwards: "We possibly edged it in the second half, when we had a lot of play and a lot of possession, so I'm disappointed we didn't edge the result, against a really good side.
"You have to be careful about being too gung-ho against Exeter because they can pick you off and catch you on the counter-attack. You have to get the balance right, and I thought we did that.
"I'm disappointed with Dave Kitson's sending-off. I felt Tommy Doherty made four or five fouls around the pitch in the first half and yet Dave was booked for virtually his first one.
"The second one was just a coming-together of players. For me, that took the gloss off what was a good performance.
"It's frustrating to lose him now because Dave had got himself into a rhythm and has been playing well lately.
"I asked for a front-foot performance from the team tonight and we got that, minus the goal. But there's not a lot wrong with our play at the moment, we're playing some decent stuff."
Exeter boss Paul Tisdale thought the Grecians' display was even more praiseworthy after all they have been through in the past few days, going from one side of the country to the other in their 4-0 win at Scunthorpe last Saturday.
Tisdale said: "Tonight was two teams playing safe football at times, and considered football. It turned into quite a strategic game out there.
"After Saturday, travelling to Scunthorpe and back, I was very pleased with all the effort of my players.
"Today it was more about concentration, a different type of game to last weekend's.
"We're not going to go far wrong if we go away from home twice and keep two clean sheets in a row.
"The league is very tight at the moment. I think it's going to be another 10 games before it opens up."
Sean Rigg twice went close for Oxford, while Ryan Williams was denied by a superb last-ditch tackle from Danny Coles.
U's keeper Ryan Clarke beat out an effort from Dave Wheeler and also saved well from Arron Davies.