Senior player Ben Clark will look after the team while the Heed search for a new manager.
Watson and number two Micky Cummins left the International Stadium to join York City on Thursday.
Clark says it was emotional saying goodbye but the club now must move on and do everything they can to earn a top seven place.
He told the club’s video service: “It was a very difficult day for everyone.
“We spoke to Steve. He told us that we have done fantastically well as a group of players and that we deserve to be where we are at this point in the season.
“He told us we can go on to achieve what we want to achieve this year. That means a lot to everyone.”
Clark added: “It always hard when a manager leaves during the season.
“But for older pros it’s not a totally new experience - it’s happened before to most of us so now we have got to work hard and move forward.
“York are a big club and it’s a great project for him. We wish them both every bit of luck at their new club.”