Sweden international Cato joined from IFK Norrköping in the summer, and has featured in all but one game in the WSL for Laura Kaminski's side.
She said: “I’m really happy to have scored my first goal, but I’m a bit disappointed that we didn’t get the three points.”
Cato opened the scoring at Villa Park on 30 minutes, passing the ball into the Villa net after she was picked out by Mille Gejl. Shortly after, Villa managed to equalise and then take the lead before half-time.
Annabel Blanchard made it 2-2 with a fine finish on the 86th minute, but Villa substitute Ebony Salmon won it for the hosts with a powerful strike in injury time.