The Addicks, who lost 3-2 to the Hornets at The Valley on Saturday, remain 12 points adrift from safety in the Championship with only 10 games now remaining.
Parkinson said: "Once we had gone 3-2 down, there was an air of resignation about us.
"Even with five minutes to go, I would expect us to be fighting to get into their box but we did not see enough of that.
"I sensed it on the pitch today and I felt the fighting spirit was lacking and we ran out of steam in the second half.
"It's a disappointing day for us after being 2-1 up at half-time and we fully deserved it.
"Having the lead at half-time when you are at home, we needed to do better in the second half but I felt Watford came out the strongest side.
"I don't feel we were strong enough as a unit and as a team and that is what has cost us.
"In the Championship, you have to stand together as a team and we showed in the first half we can play.
"But it's keeping that mentality in the second half and standing strong and doing all the ugly work, but I felt Watford we simply stronger than
Watford took the lead in the 17th minute when Don Cowie converted from Tommy Smith's cross.
But Tresor Kandol pulled Charlton level after defensive slackness from Lloyd Doyley and Adrian Mariappa.
The on-loan striker from Leeds added a second in the 33rd minute when he headed in from Matt Spring's corner.
Substitute Grzegorz Rasiak hauled Watford level in the second half with a neat finish from McAnuff's pass.
And Tamas Priskin completed the scoring six minutes from time with a measured shot after dispossessing Mark Hudson in the box.
Watford boss Brendan Rodgers recognised his side were forced to work hard for the three points and praised striker Rasiak.
Rodgers added: "We did it the hard way. We started really well and the momentum was with us for the first 20 minutes. Then we made a mistake and were on the ropes a little bit then after that.
"We got a really good goal and then conceded two goals, which we are disappointed with.
"The first goal, [Kandol] finished it well and the second goal we conceded as a collective.
"But I always felt we had the quality to come back well in the second half and won the game with two world-class finishes.
"Grzegorz is wonderful. He's a great professional. When he is asked to come in, he comes into the team with a positive attitude.
"I've worked with world-class players and seen how they finish and that was a world-class finish that got us back into the game."
This was Watford's fourth win in five league games and Rodgers added: "For the last six weeks, we have been on a real good run.
"If you take out the game in midweek [to Plymouth], the quality of football has been very good.
"What is important is that you have the characteristics to win football matches and in the last six weeks we have found the winning formula."