Though pleased with the performance against Southampton, Taylor reminded his team that last season also started brightly - and abruptly fizzled out.
"It is nice to start the season with a good win but we did that last season and went on to finish 12th, so we must learn from that," he said.
Taylor also challenged James Scowcroft to push on from a fine start that saw him notch his first hat-trick in Palace colours.
"James does not score enough goals," Taylor continued. "We had a chat in pre-season, and I told him that. It is something he has to look at.
"He wants to join in the play all the time, but he has to learn to get closer to the box and closer to the goal."
But despite his caution, Taylor admitted he was hugely impressed by the Eagles' display and revealed that his team will be spurred on by the critics who wrote them off in pre-season.
"I am delighted with this win. Southampton are going to be a very good team this season and this is a very good away win. People are saying we will finish 11th or 12th but we are looking to prove a point on that one."