The Blues’ League One automatic promotion hopes were put paid to after losing 3-2 to the Posh at Fratton Park.
Despite dominating the opening exchanges, the visitors took a 2-0 lead inside the half-hour, with Lee Tomlin and Ivan Toney scoring.
Close and Christian Burgess got Kenny Jackett’s men back on level terms, but Toney’s 75th-minute winner ended Pompey’s top-two ambitions.
They sit four points behind leaders Luton and second-placed Barnsley with one game remaining.
Close felt the Blues were the better side against Darren Ferguson’s men.
But he was downcast to see Pompey’s automatic promotion chances end.
The midfielder said: ‘The first goal was a pure sucker-punch – it was probably their first attack.
‘I was looking around at the lads and we were confident we could get back into the game.
‘Unfortunately we conceded the second and made it a bit of a mountain to climb.
‘The disappointing thing is we did climb that mountain and then we were done again.
‘We were probably the better team and it’s a disappointing one to take.
‘But we’ve really got to put it behind us and go into Saturday full of confidence.’