Harmison grabbed six wickets while left-arm spinner Panesar chipped in with three but the Durham seamer believes Panesar, the first Sikh to play for England, gets a raw deal from the crowds.
Panesar has become something of a cult hero with fans often cheering him every time he touches the ball in the field, as if surprised he hadn't fumbled.
"It sometimes upsets me a lot that people have a go at Monty. The ball goes to him in the field and the crowd laugh and cheer and this that and the other," Harmison said.
"Monty is a very good left-arm spinner. He's a No 11 batsman and the guy works so hard on his fielding, it's ridiculous.
"He's different, he looks different, everything about him is different. But he is a great member of our team.
"Every time he goes on the field, he's getting better with his batting, his bowling and his fielding. He looks the part for England."
Panesar, who achieved both sharp turn and control on the opening day of the second Test at Old Trafford, struck fourth ball on his way to a fine haul of three for 21 in 7.4 overs.
"Monty bowled an exceptional spell. He kept the men on strike for me to attack and when you get that it's nice because you haven't got work anybody over - you've done it from the previous over," Harmison explained.