The club are in danger of being dragged into a relegation battle after just one victory in 12 league games.
They face Birmingham on Saturday after a 3-0 defeat by Tottenham at the DW Stadium following a late brace from substitute Roman Pavlyuchenko.
Frustration: A clearly-offside Defoe (right) beats Wigan's Kirkland to score
Wigan were left frustrated yesterday after replays showed that the opening goal by Jermain Defoe in the 27th minute was offside.
Kirkland said: 'It is not even close. How he (the assistant referee) has not seen it, is hard to believe. It is two yards off.
'But these things happen in football. We have got to pick ourselves up and go again.
'We didn't play too well in the first half but if that effort is offside it may have been 0-0 at the break. It is bemusing.
'That is why you get frustrated. But now we have to concentrate on Birmingham now as we have 12 big games left.'
Game over: Roman Pavlyuchenko (right) scores Spurs' second at the DW Stadium
Manager Roberto Martinez added: 'We need to turn our frustration into a good reaction on Saturday.
'It is vital we carry on working hard and put in some strong performances as we are now in a crucial part of the season.'
Martinez felt his side did not get a fair crack of the whip from referee Alan Wiley. He also queried the decision to give the first goal and thought Defoe as well as Tom Huddlestone deserved red cards following separate incidents.
Martinez added: 'It is very easy to referee the two sides in the same manner. Clearly that has not happened in this match. It became quite impossible for us.'
Rubbing it in: Pavlyuchenko celebrates after scoring his second against Wigan
However, one Wigan player with a smile on his face today is midfielder James McCarthy.
James McCarthy has been called up by Republic of Ireland manager Giovanni Trapattoni for next week's friendly against Brazil.
The 19-year-old received his first call after a series of promising performances for the Latics, who he joined from Hamilton last summer.
Defoe should have seen red, fumes Wigan boss Martinez after Spurs defeatWigan Athletic 0 Tottenham Hotspur 3: Roman Pavlyuchenko conquers as Spurs go fourth and prosper from Eastlands shut-outWigan whizzkid James McCarthy handed first Republic of Ireland call up by Giovanni TrapattoniWIGAN ATHLETIC FC