Only a superb display from Griffiths secured a point for Cheltenham, who are now unbeaten in seven games.
"You take a point on the road, but with the number of chances we missed, the game should have been out of sight," Bowyer said.
"Fair play to their goalkeeper, who was outstanding with three or four brilliant saves.
"We came out and we continued from where we left off with the chances we've been creating.
"The frustrating part is we spoke about Cheltenham's strengths, with height and a real threat from set plays and the timing of their second was particularly frustrating.
"Kyle Vassell scored two very good goals and we are building relationships on the pitch. It's about gelling and getting to know each other.
"He is going to be a handful, but he can't rest on his laurels. I'll be on his back to make sure he is producing again."
Cheltenham boss Gary Johnson admitted that there was very little his team could have done about Vassell's stunning second which made it 2-2 early in the second half.
"They were all quality goals, all four of them," Johnson said.
"It was a super finish from Danny Wright after good first touch, but Billy Waters didn't get enough chances.
"There was a lot of endeavour, but because both teams worked so hard, neither team found much of a pattern.
"It was scrappy, but the goals were quality, theirs included. Vassell is a powerful lad who has played at a higher level and it was a brilliant strike from him.
"Three minutes after half-time it was disappointing to concede, but how do you legislate for that type of goal?
"The supporters backed us after the game and understood the result, we know Blackpool have been in the Championship and League One and they have players who are still at that level, physically and mentally."