The Bath coach said after the slim success on the opening day of the Aviva Premiership season: "It wasn't pretty. From where we were at half-time we did very well to bounce back.
"We had no ball at all in the first half and Andy Goode's monster right boot kept pegging us back and we couldn't get out of our half."
Worcester led 15-6 at the interval and should have been further ahead as Bath struggled to get a foothold in the match. It was a different story in the second half.
Booth continued: "We showed great resilience to get back into the game and nick it at the end.
"At half-time we knew we had to adjust and it was a complete reversal of the first 20 minutes."
Worcester had only themselves to blame for failing to win. They squandered try-scoring opportunities and did not capitalise on all their possession and territory in the first half.
Coach Richard Hill said: "We shot ourselves in both feet. It was a game that we should have won.
"We allowed them back into the game by conceding six penalties in a nine-minute period early in the second half which enabled them to draw level."
The refereeing of young Luke Pearce was a central factor in the game, which saw a penalty awarded at almost every ruck.
Hill added: "The referee was particularly hot at players not rolling away from the tackle area and those penalties cost us the game.
"Bath have the best defence in the league but we should have scored more before half-time and put them away."
The only try of the game, from James Percival 12 minutes from time, looked to have secured Worcester the game - but two late misses from Goode were crucial.
Hill added: "A little bit of composure cost us.
"We dropped the restart kick and then one of our forwards infringed on the back foot and Barkley made no mistake."
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