Andy Carroll gave the visitors the lead with a superb left-footed strike shortly before the interval, scoring his third goal in two Premier League matches against the Welsh club this season.
Bafetimbi Gomis headed goalwards from a Gylfi Sigurdsson corner in the 74th minute, with the West Ham midfielder only able to turn the ball into his own net on the line for the equaliser.
And Monk was satisfied with a hard-earned point.
"It was a hard game physically," he said. "I think West Ham always make it a hard game physically, but I thought, apart from 10 minutes in the first half we controlled the whole game.
"They actually got the goal against the run of play. That was one of our best periods.
"We were on the front foot and looking most likely to get a goal, but they scored.
"I know from their view [Carroll's] was a fantastic goal. It was a great strike, but we possibly gave him too much space when we should have delayed him and made it difficult for him to shoot.
"Again, we showed great character in the second half. We were probing and they were defending a lot deeper, making it very difficult to break through.
"We made the substitutions to give us a bit more cutting edge and managed to get a well-deserved goal.
"We pushed for a second, but I think both teams will be happy with a point."
Gomis has been challenged to grasp his first-team opportunity in the absence of Wilfried Bony, was has departed for the Africa Cup of Nations amid persistent rumours of an imminent transfer to Manchester City.
"It was a great delivery and a fantastic header from Bafe," Monk continued. "Bafe deserves that goal just for his sheer work today.
"He covered every blade of grass and was determined to help the team."
On Bony's expected departure, Monk added: "It's still ongoing. It's the same as the start of the week.
"The two clubs are talking to each other trying to finalise the matters.
"Until it's 100 per cent finalised, there's nothing else I can really say."
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