Leon Osman, Marouane Fellaini and Phil Jagielka all went close to breaking the deadlock for the hosts and the Scot was left to rue poor finishing which cost his team all three points.
He said: "It was frustrating. We had quite a few opportunities and made some chances but it was not enough, not clear enough chances really. On another day you take one and go on to win the game.
"We had three or four good opportunities to get a goal and we weren't able to take any. They did really well against Chelsea in the cup and did well again today.
"But I can't fault my boys, we made chances but didn't get behind them enough times and get the goals.
"In the main we score the goals but it was good to get a clean sheet in the end, maybe we used all the goal chances up at Cheltenham in the cup.
"I've said to the players that it's not the end of the earth. We should have taken three points but credit to Swansea they came and defended well and got a point, what they wanted.
"We had lots of opportunities in the first half, but they made it hard to play against after that and deserve a lot of credit for what they're doing at the moment."