Regan Charles-Cook's second half brace gave Woking the bragging rights - watch match highlights.
But had it not been for Cards' keeper Nathan Baxter's excellent performance, Sutton may well have been out of sight at half-time.
Despite Baxter's display, Doswell believes his side needed to be more clinical.
"We were in complete control of the first-half and we weren't ruthless enough from Tommy Wright, who had a free header and a chance from two yards," he said.
"We played against a side that wasted time from almost minute one onwards and were looking to hit us on the break. I suppose it is a compliment to us.
"I thought we played really well for 45 minutes, you can't take that away from the players. But in games like this you need to take your chances when you're so dominant in a game. We had four or five of them.
"We've now got, I think, three weeks where we haven't got a mid-week game which gives us a chance to get players back."