The Giants went down to a 24-20 defeat at the Select Security stadium despite being 16-0 in front early on in the game.
This led to the Huddersfield head coach to hoping his side can turn in a better 80-minute performance against Castleford on Friday night.
“I think we let ourselves down if I am being honest, I thought we were alright to start with and then the start to the second half just killed us,” Anderson told the club’s official website.
“The things we’ve shown there is our lack of respect in possession in the way that we just gifted the ball away and we didn’t quite do the things that we wanted to and that hurt us. The positive is that the glass is still half-full here and we still have opportunities and chance to put that right on Friday.”
The Giants’ defeat to Widnes has hampered their hopes of a late charge towards the top eight following a slow start to the season, but Anderson admits his team will keep believing until the end.
“Until it is mathematically impossible then we will keep fighting,” he said.
“The number one thing is that we have to give ourselves a chance and not worry about anyone else and we have got to make sure that we get on with our jobs and doing our roles and make sure that we execute what we do to the best of our abilities.”
Huddersfield head into this game with the Castleford Tigers on the back of a short turnaround, but Anderson is hoping to see a good reaction this weekend against a good Castleford side.
“A short turnaround can work one or two ways, you can dwell on it and decide the whole world is against you or you can roll your sleeves up and get on with it,” he said.
“They have been going alright, Daryl has got a well coached team and they can throw some things with you and play with a lot of width and a lot goes through Luke Gale, so we have got a challenge on our hands but so have they.
“We have been building for the last six weeks or so, let’s not just fall in love with the St Helens result, but two weeks before that against Leeds, the Catalans result even though we didn’t get the win. We have never had big scores put upon us, even against Wakefield on Good Friday when we were poor, we were still in it until the last few minutes.
“We just need to give ourselves a chance and keep doing things for harder, longer and give ourselves a chance.”