Earlier in the season, the Portuguese tactician had seen United drop points against Stoke City, and following his side's 2-2 draw against Mark Hughes' side at bet365 Stadium, Mourinho suggested that the Potters were playing for a draw while the Red Devils were chasing all three points in that game.
"We heard Mourinho when teams play that way [defensively] against Manchester United, he comes out after the game and says, 'We wanted to win the game and a lot of teams came for a draw.' He did the exact same thing. Mourinho criticises managers who come and play for a draw [against United], and that's exactly what he did at Anfield," Barnes told IBTimes UK.
Jurgen Klopp saw his side dominate the game at home, while Romelu Lukaku's first-half attempt was United's only real chance of scoring against the Merseyside club. Goalkeeper David de Gea's heroics against Liverpool made sure the visitors walked away from Anfield with a point.
Barnes claims Liverpool were the "better side" against United and stressed that Mourinho played for a draw and got the result he wanted against the Reds.
"Liverpool were the better side by far. Liverpool were the team who wanted to win the game, while Mourinho came for a draw. Apart from Lukaku's chance, they never had an attempt on goal," the Anfield favourite explained.
"We were slightly disappointed because Manchester United are playing really well and scoring a lot of goals. We thought they would have shown more ambition in the game. But Mourinho got the result he wanted.
"He did not want to lose and he didn't lose. But analysing the game, I feel Liverpool should have won as they were the better team on that day."
Despite Liverpool's failure to beat their archrivals after being on the front foot almost throughout the game, the former Reds winger admitted that he would always take a point against United.
"United were top of the league, scoring a lot of goals. Yes, Liverpool should have won the game, but we have got a good result against a top team," he said.
"The problem is how we are playing against smaller teams. So, a draw against Manchester United, who are now at the top end of the table, playing really well and outplaying them is a decent performance."