The Trotters were made to pay as shortly after substitute Michael Owen scored a close-range header to settle the outcome at St James Park.
Megson told Sky Sports: "We should have (won). Our work rate was good and we caused them one or two problems.
"The goal we've given away, we should be higher than that. When you're going to let balls into your area as easily with Owen around it's going to count and it's cost us.
"I didn't see the (penalty) incident. It wasn't one of Kevin's better ones I'm sure. From that point onwards it gave the crowd a boost.
"It was important we scored, we didn't and it's cost us a result. We should have got something from it. The way it was going we should have won.
"Today we had a great opportunity to win. We've not been beaten. We've thrown it away."