Aaron Mclean's injury-time strike earned Posh a creditable 2-2 draw against Paulo Sousa's side at London Road on Saturday afternoon.
"We had been behind at half-time in our two previous games and were anxious to make sure that didn't happen again," Cooper said after the match.
"A team with Swansea's footballing ability can cut you to pieces and we couldn't afford to let that happen.
"In the second half we were the better team. We got ourselves 1-0 up, should have gone 2-0 and could have been 3-0.
"You always think the game has gone when you fall behind that late, but the lads never know when they are beaten, kept going and earned a point."