Luis Suarez headed an equaliser with eight minutes remaining to cancel out Chris Herd's early first-half opener, but the Reds' attempts to collect all three points were thwarted by the woodwork and an impressive display from visiting goalkeeper Shay Given.
"I thought we deserved to win - we created a lot of chances, but we didn't finish them off," Downing told Liverpoolfc.tv.
"They took the lead and made it difficult for us. They were probably delighted with the draw, but we've stopped the losing run so that's a positive.
"Villa defended very well, but we dominated the second half and created a lot of chances. But we were disappointed we didn't start the game well enough. Villa took the lead and that gave them confidence.
"We've got to keep getting people in the box and keep creating chances and hopefully it will turn for us."