The Scotsman was inducted as part of the 2013 class in Florida on Monday night alongside former world number one and ex-Masters champion Fred Couples, former US Open champion and television broadcaster Ken Venturi, former European Tour executive director Ken Schofield and twice Open winner Willie Park Jr.
Montgomerie was an eight-time European Tour order of merit winner, had 31 victories on the European Tour and recorded five runner-up spots in the Majors among a total of 10 top-10 finishes.
However, Jacklin, who won two Majors, said he did not vote for the Scotsman and also discounted his Ryder Cup record, where he never lost in eight singles matches, as being enough to merit his inclusion.
"I vote on the basis of who’s worthy and there’s always Majors in it for me," he told the Florida Times-Union.
"He won’t be remembered for the Ryder Cup when he’s dead and buried. It will just be something that happened in a Ryder Cup. I understand he has a fantastic record and is a great player but he should have won Majors."
Bernard Langer questioned why Mark O'Meara, who won two Majors, was omitted when Montgomerie was included.
"I don’t understand why Mark O’Meara isn’t in the Hall of Fame," Langer said.
"I voted for him the last two or three years. He has the better record than either of those two. I’m not saying Couples or Monty shouldn’t be in, but I’m saying Mark O’Meara should be in."
Four-time Major winner Raymond Floyd was even harsher in his summation: "I’ll just say that you should have at least two Majors (before being allowed in)," he said.
"It takes integrity away from the term ‘Hall of Fame.’ I’m very upset at the Hall of Fame."
Montgomerie described his inclusion as a "humbling experience".
"I'm very proud to be standing here in front of you this evening," he said.
"I've enjoyed thoroughly my exploits in Major championships. I just haven't been fortunate or whatever it takes, I've never, ever stood up and made a winner's speech... I never will.
"There's always a time where a bit of fortune comes your way, whether it be for you or against your opponent at the time, and it just so happens with five runner-ups... that I just haven't been so-called fortunate to walk through the door."
Couples, renowned for being one of the most laid-back figures in the game, was overcome by emotion after being inducted.
"Thanks for taking a kid from Seattle and putting him into the Hall of Fame," Couples said as he ended his acceptance speech. "This is the coolest night of my life."