Spanish striker Fernando Torres scored both goals for Liverpool in the encounter at Anfield on Sunday.
Hodgson told Sky Sports, when asked about Torres’ fitness: “In the second half he was tired but still running, getting into positions and causing problems for Chelsea’s defenders.
“He is a vital player for us and would be any club. You can’t have success if you don’t have front players who do a good job for you.
“Hopefully at the end of the season he can say ‘even though I didn’t start so well I’ve had a good season’ and can prove it with the goals he scored.
“He wants the club to do well and can see we’re moving in the right direction.
“He couldn’t say much when the club was in the throes of being sold but like myself he sees a bright future with new owners.”
He added: “It was a very good first half performance. I thought Chelsea played well in the second half but we stayed firm and thanks to Pepe Reina and the crossbar we kept our clean sheet and had chances ourselves.
“I’m very happy with the result and the way the team responded to losing two of our back four (Glen Johnson and Sotirios Kyrgiakos) just before the game.”
