Taking charge of Pompey for the third time, Barker watched Frenchman Romain Padovani score his maiden goal in English soccer and clinch a first win since early November.
"It's a relief to have got a win at long last, hopefully it will give the players confidence and enable us to move on from here," he said.
"A win was just what the players needed, a real confidence boost for us all and one which we deserved.
"We played some good football in the first half and, in the last 20 minutes when Dagenham stepped up the pressure, showed a real desire to not allow our lead to slip away."
Padovani, a 24-year old midfielder, joined Pompey on a summer free transfer from AS Monaco and was making his first start since October.
His winner came on the stroke of half-time when the Frenchman got a crucial touch to steer a right-wing corner from Ricky Holmes past the outstretched arms of Dagenham goalkeeper Chris Lewington.
"Romain deserved his goal," Barker added. "He had a fine all-round game, covering a lot of ground and playing in the second half in an alien role to which he's accustomed.
"He looked comfortable on the ball and considering he was playing his first full league game for three months, did very well."
Barker, who summonsed his players to a three-hour Christmas Day training session, saw his chargers enjoy the lion's share of first half possession without seriously threatening the Dagenham goal until Padovani scored.
Patrick Agyemang missed a good chance, while Ricky Holmes became an increasing influence in his wide role, eventually setting up the winner.
Dagenham endured a forgettable first half, leaving manager Wayne Burnett livid at half-time.
"We were sluggish in the extreme," he fumed. "We couldn't get hold of the ball and when we did we couldn't string two of three passes together. It wasn't until the last 20 minutes we got going at all.
"Fratton Park is the sort of place our players should relish performing at. It's not often they get the chance to play in front of 15,000 and they blew it."
The ineffective Chris Dickson twice wasted chances for Dagenham, who had Pompey on the back foot as they pressed forward late in the game.
The only time Pompey goalkeeper Trevor Carson was tested came late on when he beat out a low shot from Scott Doe with his legs, but Dagenham generally lacked the energy and desire to save the game.