Davies made seven changes to the side that lost at home to Birmingham in the Premier League at the weekend.
The first time was in the 86th minute to take the game to extra-time by cancelling out Mo Camara's opener.
Then the Latvian was allowed to repeat the trick in the 120th minute to force penalties after it looked like Craig Fagan's 101st-minute header would win the game for Derby.
Davies said: "We were guilty of naivety and schoolboy errors. We have been shooting ourselves in the foot all season so far.
"After conceding early goals against Tottenham and Birmingham we spoke about starting halves right and finishing halves properly.
"We spoke about concentration and switching off and emphasised the importance of not letting the opposition get crosses in. But we did not do it again.
"It is down to mentality and character and that is what we will have to instil into the players so that they do it at crucial times in matches.
"We have got some hard work ahead of us but we will continue to develop this squad and this group of players."
Blackpool captain Michael Jackson kept his cool to score the decisive spot-kick.
Jackson stroked the ball into the bottom right-hand corner, sending Stephen Bywater the wrong way after County captain Darren Moore had dragged the previous penalty wide.