Ryan Longman curled Hull level but Townsend's strike won it in extra time.
"It meant a hell of a lot. One thing we can say is we are still fighting," Townsend told BBC Sport.
"It seems in every game this season we've given ourselves a lot of work to do - we've either gone behind early or conceded a goal at some point," added the former England winger.
"But this team has character and when we cut the silly mistakes out early in the game hopefully we can go on a run and pick up some points in the league.
"We're getting players back, we've got a big squad and hopefully we can go far in this competition too."
Substitute Townsend returned from a fractured foot to win the game and under-pressure boss Benitez, who did not risk Dominic Calvert-Lewin after his recent return from injury, also praised Gray for playing through the pain.
"We started by making things difficult for ourselves but the reaction of the team, as usual, was quite good, which means that the players care," said the Toffees boss.
"Demarai played until we had to make the substitution because he was working so hard and Andros is injured but playing because he wants to help the team. That is the spirit you expect from our players."