But the Rovers manager also admitted his team got lucky with a decision that saw goalkeeper Sam Johnstone go unpunished after hauling down Troy Deeney late in the first half as he was poised to tap home an equaliser, after Chris Brown had headed Rovers in front.
"My initial thoughts were that it was a penalty, I don't know about the sending-off, I would have to see it again," Dickov said. "I thought we got away with it.
"It was a tough game for us - Watford are a good side and they deserve a lot of credit. They worked their socks off and made it hard for us, although we looked nervy until they scored and I thought we switched off.
"But after they equalised, we got back to doing the right things and to be honest, we should have scored three or four more.
"It was a big win for us, a massive three points, but it is important not to get too carried away with it."
Brown's opener was matched by Ikechi Anya's equaliser, before Billy Sharp grabbed a stoppage-time winner for Doncaster.
Dickov reserved praise for new father James Coppinger, whose wife gave birth to a baby girl on Saturday. Coppinger, usually an attacking midfielder, slotted into an unfamiliar right-back slot against Watford.
"I thought he was fantastic," said Dickov. "We have spoken to him about that position before, especially against teams who play three up front.
"He's such a hard worker and good professional that he can easily adapt - he can play anywhere. He deserves a lot of credit."
Dickov, who revealed that Gabriel Tamas will be out injured for four to six weeks with a fractured cheekbone, also claimed Paul Quinn, a right-back by preference, was "fantastic" for playing in a centre-back role alongside Abdoulaye Meite.
Watford faced an uphill struggle after 18 minutes as Swedish striker Mathias Ranegie was shown a straight red after kicking out at James Husband.
Watford boss Beppe Sannino condemned striker Ranegie for his early dismissal, but refused to comment on the controversial incident late in the first half, that should have seen the visitors awarded a penalty and Doncaster reduced to 10 men.
"I don't like to talk about referees and we have to respect their decision," said the Italian. "I am disappointed about the red card as you always have to accept the physical contact on the pitch - I did not like his reaction."
Sannino also expressed disappointment at his side being unable to hold out for a point, but admitted he was pleased with his players' efforts.
"I was proud of them, but we are still heading back to Watford with no points. We played 10 against 11 for 70 minutes and it was harsh on us not to take anything from the game," Sannino said.
"I would like to think there was enough experience out there to manage the situation in the last 30 seconds of the game. We have to forget about this game very quickly and concentrate on the next one."
When asked if the thought the play-offs were now out of the question, Sannino said: "I have never talked about them in the past, I always said we had to take it game by game. The Championship is a very unpredictable and tough league."