Zimbabwe skipper Prosper Utseya said inexperience was to blame for his side tying with Ireland in their World Cup Group D match in Jamaica.
Ireland's White and Zimbabwe's Rainsford collide at the death
Zimbabwe needed 15 from 36 balls at one point chasing 222 to win, but were all out for 221 in a thrilling finale.
Utseya said: "It comes with experience, the more we play, people will start to relax and we'll get into situations like this and manage to pull through.
"We also gave away 15 runs at the end of their innings and dropped catches."
Jeremy Bray scored an unbeaten 115 in Ireland's 221-9 at Sabina Park, but Zimbabwe looked to be cruising to victory in reply.
Half centuries from Vusi Sibanda and Stuart Matsikenyeri left them needing just 12 runs to win off the last four overs with four wickets remaining.
However, the Africans crumbled with the finishing line in sight, Utseya hitting a full-toss straight to short cover in the penultimate over and Christopher Mpofu running himself out.
And with nine needed from the final over, Matsikenyeri missed the final delivery and non-striker Ed Rainsford was run out, leaving the scores level and Ireland celebrating.
Zimbabwe's second Group D match is against hosts West Indies on Monday.