Swansea created the better of the first-half openings in the Premier League encounter at the Liberty Stadium, with Bafetimbi Gomis missing two particularly good chances.
Jermain Defoe subsequently punished Swansea with a neat finish shortly before the break.
The hosts were again in the ascendancy after half-time and deservedly levelled through former Sunderland loanee Ki Sung-yueng's header in the 66th minute, but they were unable to go on and find the winner - much to the frustration of manager Monk.
"We had enough good chances to take the three points, the only shot they had on our goal was a goal," he said.
"I'm disappointed that we gave him [Defoe] too much space and didn't close him down well enough. It set us back because we had good chances before that and looked like being the ones who would take the initiative and take the lead.
"We had to show a bit of character and the times we moved it quickly and used one-touch football we created our best chances.
"I said at half-time if we do that in the second half we'll get a goal and push on. We got a good equaliser from Ki then we tried to push again to get the second, but it wasn't quite to be.
"Sometimes that happens. We had enough chances to score two or three today and it didn't happen."
Ki's goal came on first his appearance since returning from helping South Korea reach the Asian Cup final.
The midfielder had the ball in the net in the first half, only to be denied by a tight offside call.
"I got told his [Ki's] hairline was offside, so whether that's part of the rules I'm not so sure," Monk added.
"The angles we have on our cameras are an overview so I'll have to have another look. I'll have to tell Ki to cut his hair won't I? But sometimes you get them, sometimes you don't."
