Danny Cowley criticised referee Lee Mason after he sent off Lincoln captain Jason Shackell in the 1-0 defeat at Carlisle.
The defeat meant Lincoln missed the chance to clinch the Sky Bet League Two title and Cowley was not happy with Mason.
Carlisle midfielder Mike Jones spoilt Lincoln’s party with the second-half winner but Shackell’s first-half dismissal for two fouls on Jamie Devitt upset Cowley.
The Lincoln manager said: “Shacks only made two tackles in the whole game. The second was pretty soft if I’m honest.
“I’m pleased Premier League referees come to this level, but if they are going to come they have to respect the level and it was an arrogant display from Lee today.”
Cowley admitted: “To lose the captain after 30 minutes is always difficult.
“Credit to Carlisle because they are not easy to play against for 60 minutes.
“They have a lot of good players and combine well, but the 10 men defended heroically and but for a 25-yard strike I don’t think they would have broken down our defensive structure.”
Cowley added: “We are disappointed, but we will dust ourselves down and try to give ourselves every possible chance against Tranmere on Monday.
“The fans have been with us all season and stood side by side with us. We will respect Tranmere and we spent a lot of energy today.”
Carlisle’s winner came from Jones who drove home his first goal of the season after 75 minutes, a 25-yard right foot shot that evaded the dive of goalkeeper Matt Gilks to nestle in the bottom left corner of the net.
After a bright start, Lincoln were reduced to 10 men on the half hour when Mason sent off skipper Shackell for a second yellow card.
Four minutes earlier Shackell had earned his first yellow for a foul on Jamie Devitt, from which the Carlisle midfield man had Gilks at full stretch saving the resulting free-kick.
However, it was the second foul of Devitt that incurred the displeasure of Mason. From there Lincoln held out until Jones’ spectacular winner.
Carlisle manager Steven Pressley was happy to see his side keep alive their play-off hopes.
He said: “It was a terrific performance from us, professional and with great concentration.
“We showed real confidence and the players were magnificent to a man. The atmosphere in the stadium was electric and it was a tremendous day for us.”
Pressley added: “Sometimes when a team lose a player like they did you lose concentration, but we stayed focused and picked up our work ethic.
“It’s a really important result for us. It keeps us in the hunt.
“I think in some ways we are making progress and Mike Jones’ overall performance today was excellent. We missed his influence last week and he and Kelvin Etuhu were excellent for us.”
Pressley’s team go to Grimsby on Monday, and he said: “We have to ensure we go and play as we did today. If we do that we can go into the last couple of games with a real chance.”