The south coast club struggled to impose themselves before the break and went a goal down after 22 minutes, courtesy of Matt McClure's low swivel and shot from six yards.
Pompey rallied after the interval and, despite substitute David Connolly having a penalty saved by Wanderers stopper Matt Ingram after 70 minutes, Andy Bartram levelled matters with a powerful strike two minutes later.
Patrick Agyemang's stooping header put Portsmouth 2-1 up after 84 minutes. But Wycombe's Anthony Stewart denied the home side their first win in seven matches with a bullet header from close range in the fourth minute of stoppage time.
Awford was happy with Pompey's second-half display, but believes they were overawed by the Fratton Park roar in the first period.
He said: "The first half was not good enough. Even if we'd had a 10 or 15 per cent better performance in the first half, we'd have won that game.
"In the second half, I couldn't fault them in terms of effort, tempo and application. I don't understand how it can be so different from the first half to the second half.
"They were rabbits in the headlights in the first half. They were scared to play out there. I've spoken about it and it is an intimidating place to play for them. But it's a case of 'get used to it lads; you play for Portsmouth. It isn't going to change'.
"What a performance it was in the second half, to be fair to them. But then we just switched off at the end."
Wycombe boss Gareth Ainsworth breathed a huge sigh of relief after seeing his side snatch a late point.
He said: "I need to chill out, have a nice cup of hot chocolate and about 12 hours sleep. I am shattered! My heart was beating at the end like you wouldn't believe.
"I'm elated we got the draw, but I'm angry we played like we did in the second half.
"They camped out in our half in the second half and I was disappointed. The decisions we made in the middle of the park and the clearances we made weren't right.
"We had a plan to try and alleviate the pressure, but it didn't work. Thank goodness we had a good penalty save from Matt Ingram and Anthony Stewart's header at the end was fantastic.
"It's about time I had a bit of luck and a late goal, so I'm well pleased. I'm happy and I'm angry, but it was a good point away from home."