Stoke were perhaps fortunate to come away from the game with a point after Stephane Sessegnon wasted a golden opportunity late on for West Brom, though Stoke had their own chances throughout the game.
Stephen Ireland and Marko Arnautovic were both impressive for the home side, and Hughes was happy in general with a well-earned point.
"It was a decent, well-fought draw," Hughes told Sky Sports.
"West Brom are a good team. People have seen that before today's game, but we were unable to get a great deal of momentum.
"We didn't put them under enough pressure in the second half, but having said that Marko Arnautovic and Stephen Ireland had chances."
West Brom manager Steve Clarke was left disappointed with the decision not to award a penalty to his side after Youssouf Mulumbu was seemingly felled by Charlie Adam.
While Hughes agreed his side may have been lucky, he felt they deserved their share of fortune, especially following their late 1-0 defeat at the hands of Fulham last time out.
"Possibly, the old adage is that decisions even themselves out," he added. "It's one of those things. We had things go against us last time."
Hughes was quick to praise shot-stopper Begovic, whose man of the match performance rescued a point for Stoke on numerous occasions.
One particularly impressive stop came in the final minutes however, as Sessegnon broke through a beleaguered Stoke defence but could not find a way past the imposing Bosnian.
"He's spread himself really well. We were trying to be positive and get the three points as the home side, but West Brom are always a threat on the break.
"Sessegnon capitalised on some loose play but Asmir did really, really well.
"We're all grateful for that moment, but we know that he's a top class keeper.
"In the end we're satisfied because our keeper has made an outstanding save, which has protected what we had."
Having gone since August without a league win, Stoke's main worry could well be their lack of goals. It's now three consecutive league games since they last scored - in a 3-1 loss to Arsenal.
Remaining positive was Hughes however, who was adamant that, given time, things will click for a side who are transitioning to a new style of play.
"We keep looking at different things," he said. "We aren't a million miles away.
"We had opportunities and once we get on the end of things we'll be fine.
"Today was important to just take something out of the game."
Things get no easier for Stoke however, with a trip to Old Trafford to face Manchester United in the offing.
Although the Premier League holders are struggling under David Moyes' tutelage, Hughes anticipates a tough game, but insists his side can come out on top despite their own poor form.
He commented: "That's the Premier League for you. It'll be difficult, but maybe we'll be able to capitalise on some of their attacking play, like West Brom did against them."