However, Richard Hill's men twice had to battle before a 26-point burst in a blistering final 20 minutes saw them move clear at the top of Pool A.
"We have sat in the changing room after the game and the boys have all said how the intensity has gone up a notch in the play-offs," said Crockett, who teamed up with Dale Rasmussen in midfield.
"We won against Bristol last week with an impressive looking good score line, but it was a tough game. It was very physical and they came out to throw their weight around. London Welsh were also a difficult team to face.
"We now go to Nottingham and have got to raise the bar again. It is not going to be easy but hopefully we can get the right result.
"London Welsh came out very well and we knew they would start strong," he added. "Ultimately we kept our composure and showed some good team spirit to not panic and get the result in the end.
"London Welsh are a good team and over 80 minutes you are not going to have it all your own way. It is a matter of holding firm when they are having their good period and capitalising when you have yours.
"We perhaps gave them too long a good period, but in the last 20 minutes we turned it and scored some big points."
Crockett also paid tribute to wing Miles Benjamin after his hat-trick and admitted with Benjamin and Marcel Garvey in red-hot form the firepower in the Worcester team was causing the opposition headaches.
"The boys have all been saying in the dressing room: 'Feed Milo and he will score!' He is in good form at the moment and looks full of tries," added Crockett.
"A month ago it was all Marcel who was scoring all the tries and now it is Milo's turn. Both of them are good finishers and playing very well.
"Any turnover or space and Milo and Marc are lethal. They always take their opportunities well and I think teams are now looking at the videos and are very wary of them.
"Teams are trying to keep them quiet and that means more room for me, Razzy and others to work in. We are getting space because people are worried about the guys out wide."