The sides were level at White Hart Lane 10 days ago before Trotters midfielder Fabrice Muamba collapsed on the pitch following a cardiac arrest.
Referee Howard Webb opted to call the game off after the harrowing incident in the 41st minute.
However, Muamba has since made remarkable progress over the past week and is able to eat and speak while managing to get out of bed.
Spurs boss Harry Redknapp revealed that his players had been offered counselling following the 23-year-old's collapse.
And Parker believes the steady recovery of Muamba has lifted the team as they gear up for the rearranged game against Bolton.
When asked if the players were in the right frame of mind to face their Premier League rivals, Parker replied: "I think so.
"The game before was obviously quite tragic and something that you obviously don't want to see. But with Fabrice's recovery it has probably helped us a lot, and I'm sure it's helped Bolton as well.
"Obviously, it was a little bit tricky after what happened but I think the lads are fine now because we hear Fabrice is doing pretty well, which is pleasing."
While the combative midfielder insists he is happy to hear of Muamba's progress over the past 10 days, he knows his team-mates must not lose sight of what is at stake with a semi-final encounter with Chelsea on offer to the victors at White Hart Lane.
The 0-0 draw with the Blues at the weekend will have buoyed the players and Parker added: "The way we played at Chelsea has given us a big lift going into what is a big game for us.
"We know it's a cup quarter-final, with a Wembley semi-final against Chelsea if we win. So it's a big game for us.
"Confidence is good after Saturday's result, so we will look to go into that and win that.
"There's a big prize on offer. We would like a trip to Wembley and not just for the semi-final - we'd like to go to the final so we are looking forward to it."
